Action- Kid Icarus, Metal Gear, Mega Man, Bayonatta, Castlevania
Adventure- Zelda, Metroid
Arcade- Ice Climbers, Game & Watch, Wario Ware, Pac-Man
Fighting- Street Fighter
Health & Fitness- Wii Fit
Music-
Party- Mii
Platformer- Mario, Donkey Kong, Yoshi, Kirby, Sonic
Puzzle-Dr Mario, ROB. Punch-Out (though some would consider it sport)
Racing-F-Zero
RPG- Pokémon, Earthbound, Xenoblade, Final Fantasy, Persona
Shooter-Star Fox, Duck Hunt, Splatoon
Simulation- Animal Crossing
Sports-
Strategy- Fire Emblem, Pikmin