Note that to some extent, there
can't be simple abbreviations for every prestige class ever published, because the available letters for obvious abbreviations start to clash pretty quickly. Outside of the DMG, prestige class abbreviations are usually unspecified (and unused).
There are core class abbreviations listed in the Dungeon Magazine writer's guidelines, available here:
http://www.wizards.com/default.asp?x=dungeon/submissions
Apologizing in advance for cruddy formatting:
Abj = Abjurer (1) Adp = Adept (2)
Arc = Arcane Archer (3) Ari = Aristocrat (2)
Asn = Assassin (3) Bbn = Barbarian
Blk = Blackguard (3) Brd = Bard
Clr = Cleric Cjr = Conjurer (1)
Com = Commoner (2) Def = Dwarven Defender (3)
Div = Diviner (1) Drd = Druid
Enc = Enchanter (1) Evo = Evoker (1)
Exp = Expert (2) Ftr = Fighter
Ill = Illusionist (1) Lor = Loremaster (3)
Mnk = Monk Nec = Necromancer (1)
Pal = Paladin Rgr = Ranger
Rog = Rogue Shd = Shadowdancer (3)
Sor = Sorcerer Tra = Transmuter (1)
War = Warrior (2) Wiz = Wizard
(1) Specialist wizard classes appearing in the Player’s Handbook.
(2) NPC classes appearing in the DUNGEON MASTER’s Guide.
(3) Prestige classes appearing in the DUNGEON MASTER’s Guide.