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Of all current platforms the DS is the only answer.

For the home consoles probably 360, but Wii comes close in diversity, not in quantity.

FPS: 360 (by far)
3PS: 360 (Gears)
RPG: 360 (only platform with RPG's)
Adventure: Wii (Zelda, Zack & Wiki)
Strategy: Wii or PS3 (depends if you prefer Fire Emblem or Disgaea)
Puzzle: Wii (Mercury Meltdown, Monkey Ball etc)
Platform: Wii (Galaxy)
Racing: 360 (but PS3 comes close)

So that's equal, but since Wii seriously lacks in the FPS/3PS department, 360 wins, cause it has good games in every genre.