A Star Destroyer is a type of starship used by the Empire. They are known for their triangular shape, their ball thingies that if hit, destroy the ship (which are conveniently exposed to enemy attack, because it's not like anyone will try to shoot the thing down), carrying lots of expendable fighters and soldiers (most of the time), and their incredibly slow speed (seriously, it takes like an hour to turn it!). After rigorous testing, it has been firmly established that Star Destroyers cannot actually destroy stars.
Victory Class Star Destroyer
One of the first types of Star Destroyers, this vessel was infamous for having a top sublight speed of 5 knots. As such all of its enemies managed to stay well outside of its weapon's range, and escaped. Production was discontinued almost as quickly as it began. Also, its main weapons consisted of disco lasers that did no damage.
Venator Class Star Destroyer
The Venator Class Star Destroyer was a modification of the Victory class. While it was actually fast enough to catch opponents, and carried actual weapons, it was an extremely vulnerable warship. Its hangars were open air, an incredible feat considering it was a spaceship. This meant that the fuel and ammunition for its fighters was exposed and could be detonated simply by throwing a well placed rock. As such these ships were destroyed as quickly as they were produced, and production was discontinued after the Empire spent more than a trillion credits producing them.
Imperial Class Star Destroyer
This was the successor to the two aforementioned pieces of crap that passed for warships. These ships had actual weapons, and weren't ridiculously vulnerable. They also were a lot bigger. However these ships had a crappy power supply and was prone to power outages during the most inconvenient time. As a result the ships were destroyed while electricians were repairing them. The Empire found more use with these ships as suicide bombers rather than actual warships resulting in many won battles for the loss of a single Star Destroyer, assuming they were lucky of course.
A much more capable model, this was less prone to such power failures and as a result much better than their suicidal brothers. These were introduced after the battle of Yavin to counter the pathetic Rebel threat. Still, the ship would go ape shit if its command deck was destroyed, crashing into the nearest planet. This was shown when a little boy and an alien riding a flying bicycle crashed into the bridge of Stephen Spielberg's two hundred million credit star destroyer yacht, killing everyone on board, despite Spielberg commencing a volley of flash light fire on the UFO.
Executor Class Super Star Destroyer(*)
The Executor Class Super Star Destroyer was a massive warship, over twice as large as the Imperial Class. The cost of the vessel was also enormous at 1.56*10^93 credits and 99 cents. As such 15 were built, all of which were either destroyed during the battle of Endor or decommissioned and converted into luxury galactic cruise liners for wealthy ex imperials wishing to avoid contact with aliens in their retirement.
Vader's Executor Class Flagship
Vader's flagship was pretty much a temporary Death Star that made the triangle the scariest geometric shape around.
The Flagship's Fate
A single A-Wing fighter that lost control ironically crashed in a kamakazi fashion into the poorly protected commmand bridge.
Eclipse Class Super Star Destroyer
Despite the failure of the Executor class, the highly tenacious Empire commissioned the Eclipse class. It is the largest ship built at 17.5 kilometers the ship is completely immobile, as it was impossible to find any affordable engines because of the Executor's destruction. However, the lack of any mobility limited this warship to defending the drydock in which it still sat. The Alliance, when they reclaimed the galaxy, had to drag the huge but useless ship out of the shipyard with the force of Luke Skywalker, Darth Caedus, Anakin Solo, Cade Skywalker and the whole Jedi academy.
In short, Star Destroyers were powerful warships that were prone to many failings and misfortunes, (excluding the Eclipse, which OWNED anything stupid enough to get close). Still, for some inexplicable reason they were chosen as flagships for many famous (and infamous) individuals, like Grand Admiral Thrawn (Chimaera), Emperor Palpatine (Eclipse and Eclipse II) and Stephen Spielberg (Seven Seas).