Which computer games are good for my 2 year old?

Posted under Ask the Mediatrician.

Q: I’ve introduced my 22-month-old son to a computer program designed for babies that makes shapes and plays a sound every time a button is pushed. Lately, I’ve noticed that he is becoming more thoughtful about it. He used to just bang at the keys, but now he pushes one button at a time and watches what happens on the screen. For his birthday, I’ve been looking for an age-appropriate game that involves more thought. I have found a few games that are marked for 2 years and up, but they seem mostly targeted at kids closer to age 3 than 2. Do you have any suggestions?
Answered by Dr. Michael Rich, The Mediatrician