I've beaten:

Bonk's Adventure (Revenge, Big Adventure, CD)
Super Mario Bros. (1-3)
Super Mario World
Jackal
Darkstalkers
Street Fighter (1, 2, 3, Super, Super II, Alpha, Alpha III)
Super Bonk (1, 2)
Sonic (1, 2, 3, Knuckles)
River City Ransom
UN Squadron
Power Blade
Oregon Trail (all party members survived)

And a few others.

@ Tempest

I think you got a typo there, buddy. You got Gradius III as a game you can beat on one life. It's okay we all make typing errors. Feel free to edit your list, because beating Gradius III with one life is about as probable as someone winning a jackpot lottery three years in a row. :wink: