[coldpie]

Super Mario Land is a good place to start. The music is great, and it is very short and pretty easy.

Link's Awakening is my favorite Zelda game.

The original Pokemon games (Red/Blue, Gold/Silver) that others are recommending are pretty rough these days, but it's fun to see where it all started if you have the patience for them.

If you want something a little less well-known, Bubble Ghost is a fun little puzzler.

Regardless of what you try, remember that this is the era when game manuals were required reading since they rarely were able to fit tutorials & instructions in-game. It's good to scan through the manual first before you play something or you might be missing some critical information.