Hrmm, lessee..
2D: Tie between Super Mario World and Yoshi's Island. I don't think I can choose!
3D: Super Mario Galaxy 2, no contest! That game makes Yoshi look awesome, and he can actually swim here instead of drowning/disolving immediately in like in Sunshine.
Kart: Mario Kart DS. Although the Wii version tops this for online, this game has way better tracks. Though they could've left out ROB if you ask me.
Sport: After getting Mario Sports Mix, I can say that it's a tie between this and Mario Power Tennis.. but then again, MSM gets bonus points for allowing me to pair Yoshi and Black Mage together!
Party: Mario Party 2 of course. Those costumes were awesome, shame they never returned.
Smash (Mario's playable in it, so it's somewhat of a Mario game at least): Super Smash Bros. Brawl. Slower than Melee maybe, but I don't care, this game is awesome!