The Super Star Destroyer classes are the bigger brothers of the standard Star Destroyer
, etc.) In fact, there are not one, but three classes of Super Star Destroyer. These are the Executor-Class Super Star Destroyer
(AKA Super-class), the Sovereign-Class Super Star Destroyer
, and the Eclipse-Class Super Star Destroyer
Of these three classes, only one is actually seen in the Star Wars movies, being the Executor class vessel, named Executor (as the first of its type) , which served as the flagship of the imperial fleet at the Battle of Hoth. There is also some dispute over the exact name of the ship class, regarding if it is actually "Executor-Class" or merely a "Super Star Destroyer". Regardless of the technicalities, whenever the term "Super Star Destroyer" is used without qualification, it almost invariably refers to the Executor Class.
Size: The exact size of an Executor-Claass super star destroyer is subject to a large number of conflicting authorities. While some written references suggest it may be as small as 8km on length, others refer to it being closer to 17km, and this is backed up by analysis of the canon movies suggesting that the correct length is in the vicinity of 17km, or approximately eleven times that of a ordinary Imperial Star Destroyer. (1)
Armament: Again, the exact quantities are unknown, but at a minimum, an Executor Class is accepted to have 250 heavy turbolasers, 250 turbolasers, 250 ion cannons, and 250 concussion missile launchers. (2) However, these figures are from calculations based on the original 8km Super Star Destroyer figures, so that if the 17km size is accepted, then the actual figures are likely much larger.
Crew: 279,144 crew + 38,000 troops
Fighter Complement: The standard complement was only 144 TIE Fighters (two wings), plus many other specialised craft, but this leaves substantial spare room to permit additional ships if needed.
History: Originally two of these were manufactured, one by Kuat Drive Yards, one by Seinar Fleet Systems, both under the name "Executor". This served to mislead rebel intelligence to think there was only one ship out there, and that the claims by both yards to having constructed the Executor were merely the result of pride. However, one of the two was renamed the "Lusankya" and secretly buried under the surface of Coruscant, where it served as an ultra-high security prison, and headquarters of the evil Ysanne Isard following the fall of the Emperor. How exactly a ship 17 km in length was buried underneath a huge stack of buildings on a super-densely populated world is never revealed, and the ship is only discovered when it breaks free of the surface, killing millions, in "The Krytos Trap" of the Rogue Squadron series of Star Wars books. The Lusankya was eventually captured by Rogue Squadron in their operation to free Thyferra.
As for the Executor, as stated before, it served as Darth Vader's personal command ship. It led the effort to destroy the rebel fleet at the Battle of Endor, but was eventually destroyed when its shields were brought down by an intense bombardment, permitting one A-Wing pilot to crash his ship into the bridge, disabling the ship, and resulting in it plummeting directly into the Second Death Star.
These are not the only Executor-Class Super Star Destroyers found in Star Wars, with many others being referred to in the various books. Exact numbers constructed are not known, though some sources put the figure at approximately 10 to 12. (1)
Size: 15km (3)
Armament: 500 heavy turbolasers, 500 turbolasers, 75 ion cannons, 100 tractor beams, five gravity well generators, 1 scaled-down superlaser. (3)
Crew: 531,000 crew + 225,000 troops (4)
Fighter Complement: 35 Squadrons of Tie Interceptors, 5 Squadrons of Tie Bombers (5)
History: These craft are only seen in the Dark Empire comic books, and were in many ways a death star squeezed into a star destroyer. Its most significant feature was the scaled-down version of the Death Star's superlaser constructed along its axis. This superlaser was only 2/3 the strength of the Death Star's, so it is not quite capable of destroying a planet entirely, but is still more than powerful enough to annihalate a planet's population. Four of these were commissioned by the Emperor prior to his death (the Sovereign, Autarch, Heresiarch, and Despot), and all of these were destroyed within a year of completion. (6)
Size: Eclipse I: 17.5, Eclipse II: 16km (5)
Armament: 550 heavy turbolasers, 500 turbolasers, 75 ion cannons, 100 tractor beams, 10 gravity well projectors, 1 scaled-down superlaser. (7)
Crew: 590,000 crew + 250,000 troops (8)
Fighter Complement: 50 squadrons of TIE Interceptors, 8 squadrons of TIE Bombers
History: The Eclipse class is in many ways a slightly larger version of the Sovereign-Class, retaining the gravity generators and superlaser, but with a larger hull and larger crew and fighter completment. The Eclipse-Class was commissioned by the Emperor shortly before his death, and two were built, the Eclipse and the Eclipse II.
When the emperor was first reborn, he used the Eclipse as his flagship, and was destroyed with it when an attack he tried to send through the force to destroy Luke Skywalker turned back on him.
The Eclipse II also served as Emperor Palpatine's flagship, after he was reborn a second time. This time, he was again destroyed along with it when a rebel commando team boarded the ship and sabotaged the navigational computer, causing it crash into the Galaxy Gun, another imperial super-weapon. (9)
Just to clarify, most of this is "extended universe" canon, meaning it is not directly sourced in the movies. The reason for this is that there are only two very brief appearances of a Super Star Destroyer in the movies at all, and even then the details are minimal, so I have had to rely on secondary (the books) and tertiary (websites) sources for most of this information. As such, anything I've said it subject to a movie overruling it, but it should be noted that the books are considered canon to a fair extent.