Saw mention in the shoutbox, thought it was a neat list to see what people have ended up beating (BBH and Zerst might need 2 pages each), but anyways, I might forget some but:
I basically just included anything that flat out ends the credit upon completion of the game (or in some cases repeats infinitely).
1942
Arkanoid
Bank Panic (Repeating Stage)
Batsugun Special (1 Loop)
Buggy Challenge
Chase H.Q.
Cliff Hanger
Darius (Extra Version)
Darius Gaiden
Dragon's Lair
Crazy Kong
Donkey Kong
Donkey Kong Jr
Galaga (settings dependent)
Golden Axe
Gradius (1 Loop)
Hang On
Hishou Zame (1 Loop)
Hyper Sports (settings dependent)
Ice Cold Beer (1 Loop)
Indiana Jones and the Temple of Doom
Killer Instinct
Marble Madness
Monaco GP (game counterstops and effectively ends)
Mortal Kombat
Mortal Kombat 2
Mortal Kombat 3
Mr. Driller (1000m)
Outrun
Paperboy (Easy St)
Penguin Wars (2 Loops)
Pole Position
Pole Position 2 (Test track)
Power Drift
R-Type Leo
Rally-X Arrangement
Rod-Land
The Simpsons (JP)
Snake Pit
Spin Master
Son Son (2 Loops)
Speed Buggy (Off Road track)
Splatterhouse
Stocker
Street Fighter 2 (some various iterations)
Street Fighter 3: Third Strike
Street Fighter 3: Alpha
Super Hang On (easy track)
Track and Field (settings dependent)
Tetris Plus 2
Trivial Pursuit Bally Sente
Trog
Twin Cobra (1 Loop)
Twin Cobra 2
Vs. Super Mario Bros
Zippy Race (Repeating Stage)