Street fighter II Champion Edition - could have easily picked IIX, but this was what really got me hooked in the arcades back in the day.
GTA:San Andreas - would be a tough choice for me over Shenmue, but the game is massive and the soundtrack rocks.
Galaga - I could play this forever, r-type is a close second for my third and final game.
Honorable mention: Mortal Kombat II - best of the series and I don't know if I could go forever without actually killing my opponent ever again.