Some great games that weren't already listed:

Action / Adventure
Castlevania Dawn of Sorrow (OOE is better, but this one is also great)

RPG
Shin Megami Tensei: Strange Journey (don't trust gamespot, they don't know a thing)

Graphic Adventure/Visual Novel/etc.
Another Code: Two Memories
Hotel Dusk: Room 215
Phoenix Wright Saga

Strategy / SRPG:
Both Advance Wars
Disgaea

Other
Elite Beat Agents
Trauma Center
GTA: Chinatown Wars

I just remembered the great Soma Bringer OST while reading the previous list, it was really good.