The most powerful 'generator' on a starship is the warp core. Claims for power production vary from 1 Terawatt (Riker in an episode), through "Terawatt Range" (Geordi in another episode), "Twelve billion gigawatts per ..." (Data in an episode). The last quote is especially maddening, since we don't know "per ..." what. The term Watt is equivalent to a Joule per second, so "seconds" are already included in the definition of Watts. Also, why couldn't Data just give the output in terms of Terawatts, or Exawatts if that would be more accurate. The easiest explanation would be that the scriptwriter didn't know his Watts from his Joules, or was just wanting to "sound great" rather than impart anything realistic. However, scriptwriters "don't exist" for the purpose of this discussion. In any case 12 billion gigawatts can also be represented as 1.2E19 Watts. (12 million terawatts).

The Tech Manual for Star Trek also quotes an output in the terawatt range, but knowledgeable trek fans speculate that at cruising velocities the warp core outputs 7.1 terawatts (7.1E12 Watts) normally, and that this figure climbs as demand requires, with the warp core able to sustain an output of upto 4E16 Watts (40,000 TW) for short periods of time. This is three orders of magnitude below Data's questionable reference above.

The fuel source for this reactor is anti-matter, or specifically, anti-deuterium, which is supposedly stored in a slush form within magnetic containers aboard the starship. Note that only anti-protons or anti-electrons could be stored in a magnetic containment device, but anti-deuterium is neutral on the macro-scale, so scientifically, wouldn't really be able to be stored magnetically. Furthermore, assuming the warp core is 100% efficient:-

You could probably multiply by ten (or even a hundred) to take into account inefficiencies in the system. Note that no energy system is 100% efficient.

Generally, the Warp Core is only used for the stardrive, and the energy is NOT utilised for other ship's systems. Rather, a bank of fusion reactors are used for this purpose. The fusion reactors supposedly are not capable of producing sufficient energy to even allow the ship to achieve warp 1. If we knew what the energy requirements for warp was, we could determine an upper limit for the fusion reactors.

The most 'visible' warship in Star Wars is undoubtedly the Imperator-class Star Destroyer (colloquially known as the Imperial Star Destroyer), which is said to have a 'solar ionisation reactor', whatever that is. Star Trekkers would like to believe that this is a conventional fusion reactor. This is also indicated by one of the descriptive phrases used to describe the reactor's power output:- "equivalent to a small star". Stars are known to be fusion devices. However, given that the reactor at best would be only four hundred meters across, if it was a conventional fusion device it would be very difficult to understand how it generates the power it supposedly does. This is further compounded by the fact that the fuel source is unknown.

The power generated by the reactor is described in the following passage:

"a single hyperspace jump requires more energy than an entire planetary nation would require in it's entire history."

Since planetary nations like Corellia, Alderaan, Corellia, Yaga Minor and Coruscant are quite common, while worlds like Naboo and Tatooine are considered 'fringe worlds', this is a decidedly powerful statement. If we consider the current day United States, which consumes 1e21 Joules of energy per year and multiply by ten years, then we could say in it's entire ten year history the USA has consumed 1e22 Joules. If an ISD makes ten jumps a day, then it consumes 1e23 Joules of energy in a single day. To meet this energy demand, it's reactor would have to run at a continuous 1.1e18 Watts. However, given that the abovementioned references also goes on to say that an ISD's power core can produce more than sufficient power for all the ships systems running at full capacity *and* have a significant reserve, the ISD's power core probably puts out ten times this, i.e., about 1e19 Watts.
The Enterprise has a standard power output of 7.1 Terawatts, but can manage more than this for short periods of time. 7.1TW is about 160,000 times *less* powerful than what an ISD would need as a minimum. Anti-matter reactions just would *not* suffice as a fuel source for such a reactor. You would need to burn 223 kg of fuel per second in a 100% efficient reaction to obtain this much energy. The one exotic fuel mentioned in Star Wars reference materials is 'hyper-matter', in reference to a Death Star. No fuel is specifically mentioned in reference to an ISD. However, many people often make the statement that a Death Star does not represent anything new or different in terms of technology, just the same thing on an immense scale. If this were true, then it is not unreasonable that an ISD's primary fuel source is also 'hyper-matter'.
Exactly what 'hyper-matter' is, is unknown. Common fan theories are:-

Note that 1.1e18W is merely a minimum required output to manage 10 hyperspace jumps per day (and underestimating the amount of energy required for a jump, and that the energy is stored with 100% efficiency). Considering that utilising maximum weapons power in for example a BDZ operation alone would require the expenditure of 3e24 Joules every two seconds, or a power output of 1.5e24 Watts. However, it is unnecessary to claim such high power outputs. The cutaway diagram of a heavy turbolaser turret on an ISD clearly shows that the weapon is backed up by a bank of power cells. These power cells are used to power the weapon locally, but are merely kept fully charged by the reactor. (see diagram on Brian Young's site). There are two methods we could use to estimate the amount of energy stored in these cells.

Common reference is made in Star Wars to Power Cells. These are battery-like units which are used to power everything from hand-held blasters to lightsabres, landspeeders, pod-racers, and even as auxiliary power units on starfighters, turbolaser gun mounts, and shield generators. These units appear to be devices for storing energy which is generated elsewhere. They are quite common, can be obtained through civilian channels, and vary in size from units small enough to fit in a blaster or light-sabre, or to a size much larger than a fully grown adult (see cutaway diagram of ISD on Brian Young's site).

We know that the power cell in a light-sabre lasts for years, and is powerful enough for Qui-Gonn Jinn to have melted a man-sized hole through a three meter thick blast door in "The Phantom Menace", in a matter of seconds. To accomplish this task, the power cell would have to have a power output not less than 1 gigawatt.

Hole volume (cylinder = pi * (0.5m)^2 * 2m)         1.57 m3
Density                                             7700 kg/m3  (Assuming Iron, not steel)
Specific Heat Capacity                              447 J/kg.K  (Assuming Iron)
Initial Temp of blast doors                         300 Kelvin  (Room temperature)
Final Temp of blast doors                          1850 Kelvin  (Low melting point)
Energy required for the task                        8.4 Gigajoules
Time frame of operation                               7 seconds
Average power output                                1.2 Gigawatts

Another power cell, slightly larger, was handed by Qui-Gonn Jinn to Anakin as a means with which to power his pod-racer. The pod-racer utlises repulsor-lift technology to remain 'air-borne', probably weighs between 200kg and 500kg, has a top speed of 947km/hr (Incredible Cross Sections), and can accelerate to this top-speed in seconds. I have no idea how to calculate the power requirements for this performance (especially the repulsor-lift part). I will add this as soon as ideas start flowing.

We know that individual compartments of an ISD are designed to function independently, so that damage to any one section does not cripple the entire ship. From the cutaway diagrams we also see that individual compartments have their own auxiliary power cells. Not all compartments operate at peak performance all the time, and the ship could go into battle at a moment's notice, thus instantly changing the energy profile of the ship. It is unlikely that the ship's power core is yo-yo'd up and down all the time to satisfy this need. The most likely power distribution model would be for individual systems to draw power from local banks of power cells, which are kept fully charged by the power core.

This would allow any compartment to have a drastically fluctuating power requirement, without having a noticeable impact on the reactor core. So in effect, the power cells would serve as a 'buffer', handling short-term power requirements, and when power requirements are reduced, the buffer could be recharged by the reactor core. This would allow the reactor core to dedicate itself to the most important task at hand, the propulsion of the ship, while 'excess power' is used to keep the multiple banks of power cells fully charged. With a motive power of 1e19watts (reactor minimum), and an acceleration calculated by Mike Wong to be 30km/s^2, this would allow for a mass of about 9 thousand tons for an ISD, which seems very light. If engine power is much higher, the shield recharge rate would approach realistic levels, as would the mass of the ship, so this engine power must be an absolute minimum.

In times of great need, power might be shunted from non-essential power banks to other ship's systems. This would allow for e.g., the shields to draw power from life-support systems, or the weapons (in a BDZ operation) to draw power from the power banks supplying the shield generators.