Granted, some are obscure and/or dead/dormant, but still.
Platformer - Super Mario Bros., Donkey Kong Country, Yoshi's Island, Wario Land, Kirby, Kid Icarus classic, The Legendary Starfy, Drill Dozer, Ice Climber
Action-Adventure - The Legend of Zelda, Freshly-Picked Tingle's Rosy Rupeeland, Metroid, PokePark, Pandora's Tower, StarTropics, The Mysterious Murasame Castle, For the Frog the Bell Tolls
Action - Hyrule Warriors, Pokemon Rumble, Kid Icarus: Uprising, Custom Robo, The Wonderful 101, Disaster: Day of Crisis, Zangeki no Reginleiv, Sakura Samurai, Steel Diver, Battle Clash, Balloon Fight, Balloon Kid
Racing - Mario Kart, Diddy Kong Racing, F-Zero, Kirby: Air Ride, Wave Race, 1080°, Excite series, Pokemon Dash
Space Shooter - Star Fox, X/X-Scape
Fighting - Super Smash Bros., Punch Out!!, Pokken Tournament, ARMS, Joy Mech Fight, Teleroboxer, Urban Champion
Turn-based RPG - Paper Mario, Mario & Luigi, Pokemon, Mother/EarthBound, Tokyo Mirage Sessions, Golden Sun, Magical Starsign, Glory of Heracles, Fossil Fighters, Marvelous: Mohitotsu no Takarajima
Action RPG - Pokemon Ranger, Xenoblade Chronicles, Ever Oasis, The Last Story, Soma Bringer
If they had the resources, they could support a console all by themselves if they wanted to (though one could argue that they did with the Wii U towards the end of its lifecycle) ---