There're some general classes of characters you know about:

Blaster - Fires ranged attack. Has wire hook for grappling. Default characters include any one with a gun. Customizable from the cantina station. Note the character with the revolver type weapon has the shoot dodge (and rapid fire) ability.

Jedi - Engages lightsaber melee attack. Has force powers. Can double jump. Default characters include Luke (Jedi), Yoda, Vader, and Kenobi. Customizable from the cantina station. Note saber color determines Force alignment for customizable characters, but the Maul head also affects alignment.

Dark Jedi - As Jedi but can affect Dark Side objects. Vader is default. Note saber color determines Force alignment for customizable characters, but the Maul head also affects alignment.

Ghost - As Jedi but enemy does not attack (as per disguise rule).

3PO - Droid 3PO can open 3PO doors and switches. Most useless character of your party, apart from opening doors. Unavailable as custom character.

R2D2 - Droid R2 can open R2D2 doors and switches. Hovers short distances (same as Fett's jetpack). Electric probe can also stun enemies. Unavailable as custom character.

Kid, midget or amputee - Can go through kid-tunnels to reach secret areas. Unlike the old class, this version can fire like the blaster class, but cannot do so when moving or jumping. Default characters are Wicket and the anonymous Ewok. This class is not available from custom mode.

Stormtrooper (Imperial) - Can go use Imperial doors and switches. This is part of the disguise factor. Note not all characters can use the disguise station. Available from the cantina station. Default character is Vader. More available from the shop.

Bounty Hunter - Can go use Bounty Hunter doors and switches, and may create a remote bomb for destroying shiny metal objects for extras. Default character is Leia (Bouush) and more can be found in the shop. This is also a part of the disguise factor. Note not all characters can use the disguise station. Unavailable from the customization mode.