Prestige Classes
Prestige Classes offer a new way to multiclass. Typically, when you hit 5th level, provided you have met specific requirements for the class, you can switch over to a prestige class. You would start at 1st level in the Prestige Class, but keep your old levels and in most cases your old abilities (that can vary for some prestige classes). Your combined level would be the addition of any of your multiclass levels (if you have any) plus your prestige class levels.
Prestige Classes were introduced in the Dungeon Master's Guide and continued in other supplements. Prestige Classes have many advantages, that's the whole idea of why they were created. However, taking a Prestige Class delays your ability to make multiple attacks per round and it can delay an increase in your spellcasting ability (the feat Practiced Caster can help with this up to 4 levels).
 
New Character Classes
The Ninja in the Complete Adventurer is a broken character class and is not allowed. All other classes presented in the core rules, Complete series or other supplements, except for those from campaign settings (Eberron, Forgotten Realms, Ravenloft ect.) are allowed.
Archivist (H. of H.) Duskblade (PHB2) Ninja (native to Rokugani) Soul Knife (Exp. Psi.0
Ardant (C. Psi.) Factorm (Dungeonscape) Paladin (PHB) Spellthief (C. Adv.)
Barbarian (PHB) Favored Soul (C. Divine) Psion (Exp. Psi.) Spirit Shaman (C. Divine)
Bard (PHB) Favored Soul (Miniatures) Psychic Warrior (Exp. Psi.) Swashbuckler (C. Warrior)
Beguiler (PHB2) Fighter (PHB) Ranger (PHB) Warlock (C. Arcane)
Cleric (PHB) Healer (Miniatures) Rogue (PHB) Warmage (C. Arcane)
Divine Mind (C. Psi.) Hexblade (C. Warrior) Samurai (native to Rokugani) Warmage (C. Arcane)
Dragonfire Adept (D. Magic) Knight (PHB2) Scout (C. Adv.) Wilder (Exp. Psi.)
Dragon Shaman (PHB2) Lurk (C. Psi.) Shungenja (native to Rokugani) Wizard (PHB)
Dread Necromancer (H. of H.) Marshal (Miniatures) Sorcerer (PHB) Wu Jen (native to Rokugani)
Druid (PHB) Monk (PHB)    
       
Notes:
(C. Adv.) = Complete Adventurer
(C. Arcane) = Complete Arcane
(C. Divine) = Complete Divine
(C. Psi.) = Complete Psionist
(C. Warrior) = Complete Warrior
(D. Magic) = Dragon Magic
(H. of H.) = Heroes of Horror)
(Miniatures) = Miniatures Handbook
(PHB) = Player's Handbook
(PHB ) = Player's Handbook 2
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