Emmett, my 3 year old is the biggest player of app based games in our house.
His current favorite is a game called "Where's my water". It can be found in the Android Market for like $1.  The game is really neat. Basically, you have to problem solved in creative ways. The goal is to get the water to the alligator so he can take a bath.
Emmett loves this game and is really good at it.
There are a ton of levels to play and the developer is adding new levels frequently.
Check it out......
Download from the Android Market: Where's My Water
