2D Platformer/Sidescrollers:
-Castlevania: Dawn Of Sorrow (Castlevania games aren't for you? Forget it because this game can make you change your opinion)
-Castlevania: Portrait of Ruin
-Castlevania: Order Of Ecclesia
-Contra 4
-N+ (if 2D platfmormers is a good thing for you, you should give this game a try on xbox live or DS)
-New Super Mario Bros.
Action:
-Geometry Wars: Galaxies
-Grand Theft Auto: Chinatown Wars
-Metroid Prime Hunters
-Ninja Gaiden Dragon Sword (nice gameplay and graphics for a DS game)
-Space Invaders Extreme 2
Adventure Point and click:
-Hotel Dusk (incredible game)
-Phoenix Wright: Ace Attorney (This is one of my favorite franchises this generation)
-Professor Layton and the Curious Village
-Time Hollow
Puzzles:
-Planet Puzzle League
-Tetris DS (I am not a Tetris fan but I really like this game)
RPG:
-Chrono Trigger (if you never played the original game or the psx game)
-Dragon Quest IV
-Dragon Quest V
-Final Fantasy IV
-Mario and Luigi: Bowser's Inside Story
-Shin Megami Tensei: Devil Survivor
-The Dark Spire (if you want to play an old school RPG)
-The World Ends With You
Tactics:
-Final Fantasy XII: Revenant Wings (storyline is meh but it's a good game)
-Luminous Arc (similar to FFT but it's more simple and has a better storyline)
Rhythm:
-Elite Beat Agents (awesome game but I prefer Ouendan, so if you can import games and you like japanese songs, give Ouendan a try)
-Rhythm Heaven (hard but very addicting)
Simulators:
-Trauma Center (yeah, it's veeery hard, but I like it)
-Trauma Center 2