Mmmm...I play mostly pc games,but super mario 2 0r 3 for the nes,or super mario world for the snes are good ones. If you want to get into a storyline and you prefer roleplaying games, I'd say final fantasy 6, which was released as final fantasy 3 for the snes in the US. Tetris is good if you don't really want to be too involved,Legend of Zelda Link to the past for snes is a good combination of action and roleplay.
EDIT: and for pc, the original fallout or fallout 2 were always favorites of mine. I enjoy the splattering sound your enemies make when you score a critical hit with a machine gun,it's very therapeutic.