I remember seeing a sesame street series of games for nes, snes, and probably more recent systems too. Also, Mario Party if you have an emulator that plays it, and I second the motion for puzzle bobble. Very colorful, disgustingly cute characters.
On Mame, look for "Wacko" it looked like a good colors / shapes matching game, and has in-game play instructions.
Super Gem Fighter Mini-Mix.
Super Dodge Ball (the 1996 one, sdodgeb not spdodgeb)
The Simpsons, a 2-year-old could have fun watching the characters move around even if they didn't even know they were supposed to press the buttons too.
Roc'n Rope, Dig Dug, Galaga, all don't require a lot of coordination to have fun.
"Blue's Journey" is great. Forgiving gameplay, colorful & nonviolent. (bjourney)
Waku Waku 7 is a nice kids' fighter. (wakuwak7)
Three Wonders is nice. (3wonders)
"Shocking" is great.
Space Invaders 95 is good. (spcinv95)
Pnickies, if there's an english version... if you're above reading age...
"Armored Warriors" (armwar)
Asterix & Obelix (asterix)
Magical Crystals (mgcrystl)
Ninja Baseball Batman... if you can stand the music without shooting yourself. Good 4-year-old sense of humor.