As far as real science knows, there is no practical way to exceed the speed of a photon in vacuum. A photon is the purest form of energy, and has zero rest mass. In other words, it's energy to mass ratio is near infinite, and 300,000 kilometers per second is the velocity it achieves in the total absence of any impediment. By definition, any object which has mass therefore cannot have a better energy to mass ratio than a photon and therefore will never be able to match the speed of light. In all space-operatic science fiction, mechanisms are 'invented' by which inter-stellar journeys can be completed in a time less than that required by the purest form of energy, light. Any discussion as to the nature of such inter-stellar drive mechanisms therefore would be pure speculation and total fantasy.


Nature of Warp Drive
Exactly what warp-drive is, or how it (fictionally) works is not explained to the audience. Various fan-theories abound, with the general common thread being that the fabric of the universe (the space-time continuum) is 'distorted' to bring the destination closer than what it actually is. The area of distortion is limited to the immediate surroundings of the starship. So by way of gross example, if the distortion extends one hundred meters ahead of the ship, the ship only has to travel 10 meters to reach the head of the distortion, hence although it is travelling at speed X, it is actually travelling for distance 10X. This distortion is continually propogated ahead of the ship as it moves. The closest real-science theory which deals with warp drives postulate that the distortion itself cannot be propogated faster than the speed of light anyway, and that to accomplish this would require an unspecified quantity of matter with negative mass. Note that anti-matter does not have negative mass, it has positive mass but opposite 'spin' (charge).
Note that a gravity well can be thought of as a space-time distortion as well. Exactly how the distortion created by a warp drive would differ from a gravity well is not known. It does seem reasonable to postulate that two distortions of space time occuring in the same position in space would interfere with each other. It is quite logical therefore that warp drives would suffer interference from interactions with gravity wells. Evidence for this can be found in two episodes [names to follow later]. In a DS9 episode Worf prevents a group of Jem'Haddar ships from engaging warp with an 'inverse graviton beam', and in a TNG episode the gravity of an uncharted Dyson sphere brings the Eterprise out of warp and prevents it from using warp until it has cleared the area. In various other episodes (TNG and VOY) quantum singularities of varying natures (black holes) prevented use of warp as an escape mechanism though it was not implicitly stated that extreme gravitational distortion was the cause. Presumably a starship finding itself inside the event horizon of a black hole (the mathematical boundary beyond which photons cannot escape the gravity well) could still use a FTL drive to escape where a photon couldn't.
It is also an established trend in TNG that starships use Impulse drive to navigate star systems, and warp drive to navigate Inter-stellar space. In several episodes (even those where speed was of the essence), Warp drive was disengaged when entering star systems and the final approach was made at Impulse speeds. On rare occassions (when the ship is in extreme danger) we see warp drive being engaged inside a star system, so it is possible, but would presumably place a greater strain on the warp drive.
Whether the mass of the starship itself influences the amount of energy required to distort spae-time is unknown, though it is logical that ANY mass within the confines of the warp-field has to distorted as well as the vacuum, therefore mass entering or leaving the warp field will have a definite effect on the warp-core sustaining the field.

Energy Requirements
It takes a continual application of energy to maintain the warp field (space-time distortion). The power output of the ship's fusion reactors are either incapable of producing the power required, or there is something about the nature of their operation that precludes them from driving the ship at warp. This job is left to the 'warp-core', which from various comments on-screen is a matter-antimatter reactor, specifically a deuterium-antideuterium recator.
In real-life, there would be little to set a M/AM reactor apart from an ordinary fusion reactor. The power output of any fusion reactor is directly proportional to the number of inter-atomic collisions which can be sustained. In theory the chance of a reaction is much higher in a M/AM reactor, but there are problems with fuel storage, and additional logistical problems in transporting and storing fuels which are inherently and dangerously reactive, hence several exploding warp-cores in the series.
There is very little in the way of corroborating evidence to support power output claims for the warp core. In one episode Data does supposedly provide a power output, but in a totally irreconcilable unit of measurement (Watts per second). Assuming he meant Joules per second, then his claim was 12.75E18 Watts. However, Riker and Geordi in other episodes made claims of Terawatt level power output (1e12 Watts to 1e14 Watts [100 Terawatts]).
There is one way to reconcile Data's quote. The units he used was watts per second, which would describe a ramp-up curve for power production (i.e., the rate at which the engine was being revved up). If this was a steady state measurement, then the warp-core would have exceeded Riker and Geordi's claims in a microsecond. To reconcile all their statements, we might assume that the warp-core does not produce power in a steady state, but operates like a dynamo producing an alternating current. In this case Data might have been describing the slope of the curve describing the power oscillation, which would be based on the number of reactions per second (anti-matter pellets being injected per second?). Without an amplitude for the oscillations though we wouldn't be able to calculate a steady state power output.

From Voyager we learn that hard course changes at warp are not possible "Faster than light, no left or right." (Paris). For such course changes, it is necessary to disengage warp, re-orient the ship under Impulse power, then re-engage warp. However, we have seen gentle course changes in many episodes (external shots). Although it is necessary to lay in a course before engaging warp, propogation speeds are sufficiently slow so that potential hazards can be detected and avoided using sub-space detection equipment. See sensors. Theories vary as to what would happen should the ship collide with even a small object. Simplistic Newtonian mechanics would seem to indicate that even a small asteroid colliding with a starship would impart immense amounts of Kinetic Energy. This is incorrect. The physics of space inside a warp field appears to be the same as that utside the field, except that the frame of refernce has altered. Inside the field, people can see each other even though the ship is travelling faster than light. Everything inside the field behaves exactly as if the ship were travelling slower than light. When any object crosses into the warp-field it's behaviour is determined by the physics of the warp field. Firstly, it's velocity with respect to an arbitrary point outside the field would be the same with respect to an arbitrary point inside the field, except that the field is moving. Hence, only the frame of reference has changed. Secondly, it would place a load on the warp field generator proportional to it's mass. Should it have large mass, it might place a severe strain on the warp-core to maintain the same field strength.

Notable Quotes
We have various incidents in Voyager and TNG where warp factors are directly equated to real-space velocities.[Most of these quotes were gleaned from Mike Wong's database.]
1. Voyager was "displaced" to a point 70,000 light years from the nearest Federation base, and estimates that it will take them 70 years to reach Federation space. That works out to an average/cruising velocity of 0.114 light years per hour, and will require several re-fuellings.
2. "Encounter At Farpoint". "DATA: Projection, sir. We may be able to match the hostile's nine point eight, sir. But at extreme risk.". Is warp 9.8 "maximum warp"?
3. "Where None Have Gone Before". Geordi claims that the Enterprise-D could travel 2.7 million light years in 3 centuries at "maximum warp", for an average velocity of 9000c. 9000c is roughly 1 light year per hour. It is unknown how long "maximum warp" can be maintained without permanent damage to the warp-core or without re-fuelling.
4. "Q Who?". "DATA: At maximum warp, in two years, seven months, three days, eighteen hours we would reach Starbase one eight five." This after they had been hurled 7000 light years by Q. They were inside Federation space before the incident, therefore the max distance to the Federation is 7000 light years. This is an average velocity of 2700c, or 0.3 light years per hour. Note the difference in velocity between the last two points. Perhaps local galactic conditions would impact on the real-space speed equivalent of maximum warp. Note that in point 3 the Enterprise would be crossing largely inter-galactic space, hence would be able to travel in a straight line and have fewer local gravity distortions to contend with.
5. "Survivors" "GEORDI: Yes, sir. I'll get you to Nine point three seven in fifteen seconds." [MJ: from warp 5.5] The ship cannot dial any warp speed indiscriminately, but slowly climbs the scale.
6. "The Price" "PICARD: It would take us nearly a century at warp nine to cross that distance... " [MJ: 70,000 light years.] This puts warp 9 at about 700c, or 0.08 light years per hour. Remember the warp scale is a logarithmic scale, so warp 9.3 or warp 9.5 could be much faster. Presumably warp nine is the highest safe cruising velocity of the Enterprise.
7. "Tin Man" The Enterprise slows down significantly as it approaches the outer edge of a star system even though it is racing a (cloaked) Romulan vessel to the destination.
8. "The Most Toys" "WESLEY: The Jovis has a maximum speed of warp three. He's had 23 hours, so we can define a perimeter of .102 light years as his possible range." Warp 3 is roughly 39c, or 0.004 light years per hour.
9. "Legacy" "DATA(in ref to the warp drive): Stable. But we have maintained warp factor nine for longer than is recommended.". Mmmmmmm.
10. "Clues" Riker mentions that 0.54 parsecs is "almost a day's travel." Thats 650c, or 0.07ly per hour, at what was presumably cruising speed. Enough said.


Nature of Hyperspace Drive
Hyperspace (in Star Wars) appears to be used in reference to a "non-reality" or "alternate dimension" in which the laws of physics are drastically different. Hyperspace (like Sub-space) appears to have a one-to-one relationship to real-space, in that objects in real-space and hyperspace at the same "position" can interact with each other. Ships travelling in hyperspace can vary their speed, but generally travel at speeds faster than Star Wars sensors can match. This means that ships are essentially 'blind' in Hyperspace, and routes or jumps are plotted in advance to avoid collisions. Ships also rely on 'safety-cutouts' which disengages the hyperdrive motivator when a strong enough 'mass-shadow' is encountered. An old Victory-class destroyer with a relatively poor engine (class 2.0) is implicitly stated to be able to achieve a Hyperspace velocity 'equivalent to 127 light years per hour' in the book Dark Force Rising, and backed up by various official sources and publications. This is slower than speeds achieved in the movies, where characters travelled from a core system (Coruscant) to an Outer Rim system (Tatooine) in a day or two. This would require speeds of upto ten times faster than a class 2.0 hyperdrive can attain. The Falcon for example, has a class 0.5 hyperdrive, which is much faster than a class 2.0 drive (the smaller the number, the faster the ship).
In various novels, ships in hyperspace were mentioned to have changed course after intercepting communications. This implies that a course change in hyperspace is possible. Notably, Lando intercepts a communication between Imperial ships warning him of an impending ambush in The Courtship of Princess Leia causing him to initiate a last-minute course change. This is significant also to point out that ships in hyperspace are not incommmunicado. It is quite conceivable though that range and direction would limit the degree to which they can maintain external communications.

Hyperdrive outclasses warp drive on the strategic scale, in the sense that ships in 'hyperspace' cannot be effectively tracked, and appear to be inherently cloaked. Ships employing hyperdrive can also cross the entire Star Trek galaxy in days, hopping from star system to star system in minutes, whereas the fastest ship in Starfleet (Voyager) is faced with a prospect of a seventy year journey merely to cross half the Milky Way galaxy.

It would take a year for a decent Starfleet vessel to cross 'Federation Space', which extends for 10,000 light years and encompasses a mere 150 worlds (Picard, "First Contact") while a hyperdrive vessel can do it in three or four days.

Warp-equipped vessels can engage each other at warp speeds, usually in a pursuit situation where both are travelling at a fixed velocity relative to each other, and in a straight line. Full warp combat, where both ships take full evasive action, has never been seen. It is also known that ships at warp cannot target (or hit) ships not at warp, most likely due to the extreme speed differentials involved. Vessels in Star Trek always engage each other at sub-warp speeds, from relatively stationary positions, and continue shooting until one or other is destroyed. It is rare for ships to attempt an 'escape' at warp, to avoid destruction. Also, warp-capable ships attacking the stationary DS9 attacked the station at sub-warp velocities, and were destroyed, when attacking the station at warp velocities would have meant they could evade weapons fire, or possibly stay out of range.
Given that warp does not allow for much manoeuvering, a torpedo fired at warp would be a near dumb-fire, or possibly only able to execute the most rudimentary course changes. Hitting even a slow-moving target would be near impossible, especially as the firing ship would have to line up the shot to perfection (within a few billionths of a degree over normal combat ranges and launch the torpedo with timing accurate to billionths of a second. Hyperdrive does not allow ship-to-ship combat at all.

For this reason it is believed, that should a ship-to-ship battle occur, it would have to be at sub-warp velocities, although there is the potential for damaged vessels to 'escape' to hyperspace or warp, where an engagement between the two are unlikely. A big unknown in Star Wars is the use of hyperdrive equipped missiles. While used by the Galaxy Gun missiles, and known to be small enough to fit on probe droids (Empire Strikes Back) they have never been seen to be used as an anti-ship weapon.

In Star Wars, ships are known to 'trap' each other with 'interdiction fields', presumed to be an 'artificial gravity well' or a 'mass shadow' projected into hyper-space but not real-space. Since no actual gravitic effects are observed it is quite possible that the effects are limited to hyper-space. [Mention has been made to me of an event in a novel I have not read, where a moon's orbit was adjusted through the use of an Interdiction field.] It is known that ships engage their hyperdrive in close proximity to large gravity wells at great risk, although a single planetary diameter is considered sufficiently far away for a safe jump. From this, we can deduce that a hyperdrive motivator of given power can launch a ship of given mass into hyperspace provided it can overcome local space-time gradients.

The argument has been made that a starship could extend it's warp field to achieve the same effect as an interdiction field, but this assumes that the warp field creates a space-time distortion, that it can be extended very far from the source starship, and that the gradient of distortion is sufficient to overcome the capability of the hyperdrive motivator. In one episode of DS9, an 'inverse graviton beam' was used to prevent a handful of Dominion starships from going to warp. It is unknown whether this effect would work on all warp engines, how powerful a beam is required, or whether in fact it is anything like the 'mass-shadow' effect of an interdiction field.

Opinions as to how interdictors compare to 'inverse graviton beams' vary. In Star Wars, it is known that 'immense' power is required to generate these fields, which is logical. Conservation of Energy implies that to project a mass shadow across a region of space large enough to encompass a major fleet battle the projector must be an energy source AT LEAST equivalent to the mass being simulated. Since no system is perfect, inefficiencies in the system might require a much greater energy source to simulate a relatively small mass-shadow. If a space battle were to occur for example over a range of a few tens of thousands of kilometers, then a planetary sized mass would have to be simulated to contain the battle. Given that Star destroyers have power generation capabilities several orders of magnitude greater than anything the Federation can manage, and that these Star Destroyers do not have enough power to create the required interdiction fields, it is unlikely that any Federations ship can create such a field. A low-powered 'inverse graviton beam' may not be sufficient, as hyperdrives can be engaged in close proximity to asteroids, other vessels, small moons, and with a high measure of risk, even within the atmosphere of planetary bodies (deep inside the gravity well).

In some episodes of Star Trek, notably Star Trek V, the Enterprise, with Kirk at the helm, travelled to the centre of the galaxy and back in days (possibly weeks). Yet Voyager is unable to cross only half the galaxy given decades in which to do so, fuel considerations aside. These 'variations' in warp-speed is explained as being due to ships exploiting short-lived 'warp lanes', which facilitated faster travel along particular routes due to temporary sub-space conditions. These 'lanes' are still used to explain away inconsistencies in the on-going saga.

In "Star Wars: A New Hope", Han is heard to quote the Millenium Falcon's top-speed as "point five past light". Some detractors have taken this to mean "one point five times light-speed", which is blatantly impossible, since Han could not have travelled from one star system to another in anything less than several years at this speed. Furthermore, Han goes on to say that he has been "from one side of this galaxy to the other", which while open to interpretation (a spiral galaxy is flat, he might have meant the short side), it would still imply a journey time of thousands of years. The explanation is given as hyperdrive engines being rated on an inverse logarithmic scale, with speeds getting exponentially faster as zero is approached. Most hyperdives are rated in the range from "class two" to "class point five", with "point five" being faster.

Another interpretation is that 'light-speed' is the colloquial term used in Star wars to describe the threshold between real-space and hyper-space. Once the light-speed barrier has been exceeded, conventional physics no longer applies, and the term 'point five' may have direct bearing on the tachyonic measurement required to get a velocity equivalent. It may mean (my interpretation) the accuracy or perfection of the hyperdrive motivators in converting the starship sub-atomically to a tachyonic equivalent of their real-space counterparts. The more 'accurate' the conversion into a tachyonic state, the greater the real-space velocity achieved. This would also explain why faster ships have engine ratings approaching zero. It is possible that zero is unattainable, just as warp 10 is unattainable.

It is also known that hyperspatial speeds are not fixed, ships can vary their velocities, travelling faster along well patrolled routes between popular destinations, but slower through unmapped territory. This variation of velocity is scaled differently, with "point four" being slower than "point five", and only the fastest ships being able to achieve anything better than "point five." This measurement scale is probably as a result of writer error (confusion between class ratings and velocity), but if writers "don't exist" then there are two measurements for hyperdrive speed ratings, the engine category, and the speed being utilised. In novelisations, "point five" is implicitly translated as equivalent to one hundred and twenty seven light-years per hour, for a ship which has a class 2.0 motivator.

In the movies, various characters traversed great distances in ridiculously short times. In "The Phantom Menace", Darth Maul travels from Coruscant (a core world) to Tatooine (a rim world) in the space of a day. He leaves Coruscant after Anakin tells Qui-Gonn the pod-race is "tomorrow on Bunta's eve", and arrives the night before the race. If the distance between the two worlds is thirty thousand light years, then Darth Maul would have had to travel at over a thousand light years per hour for at least twenty four hours. His ship has a class 3.0 hyperdrive, supposedly much slower than the class 0.5 motivator on the Millenium Falcon.
Yet another explanation for these hyperdrive factors appears in a role-playing game where it is used as a journey-time multiplier. The rule proposed is that a ship with a class 2.0 drive will take double the time to complete the same trip as a ship with a class 1.0 motivator, while a ship with a 0.5 motivator will take half the time. The system was at least consistent within the game.