There are countless number of games.
There's Mario Bros., Pinball, Golf, Wrecking Crew, Super Mario Bros. 2, Dr. Mario, NES Open Tournament Golf, Family Computer Golf: Japan Course, Family Computer Golf: U.S. Course, Famicon Grand Prix: F-1 Race, Famicon Grand Prix II: 3D Hot Rally, Kaette Kita Mario Bros., Mario Paint, Mario & Wario, Undake30 Same Game, Mario's Super Picross, BS Super Mario USA, Excitebike: Bun Bun Mario Battle Stadium, Mario no Photopi, Super Smash Bros., Dr. Mario 64, Mario Artist: Paint Studio, Mario Artist: Talent Studio, Mario Artist: Communication Kit, Mario Artist: Polygon Studio, Luigi's Mansion, NBA Street V3, SSX on Tour, Dr. Mario Online Rx, Super Mario Land, Super Mario Land 2: 6 Golden Coins, Picross 2, Game & Watch Gallery 3, Mobile Golf, Mario Family, Super Mario Advance, Mario vs. Donkey Kong, Game & Watch Collection, Mario vs. Donkey Kong 2: March of the Minis, Game & Watch Collection 2, Mario vs. Donkey Kong: Mini-Land Mayhem, Dr. Mario Express, Mario Calculator, Mario Clock, Mario's Cement Factory, Manhole (Game & Watch), Helmet (Game & Watch), Chef (Game & Watch), Vermin (Game & Watch), Luigi's Mansion: Dark Moon, Mario and Donkey Kong: Minis on the Move, and Donkey Kong.
Luigi's Mansion does have a Bowser appearance, in a sense...You fight a giant fake version of him as part of the battle with King Boo. Technically not the real Bowser, but still... 03:22, November 16, 2013 (UTC)