I will add the new recommendations here to the other thread. For a 3 year old, I recommend these as possibilities, in no particular order:
Clever Castle (single player)
Rush Hour Jr. (single player)
Topitop (the snowman one is way cuter, but both versions are the same gameplay-wise)
Carcassonne (a three-year-old can have fun playing this, though the totalling up may have to be done by someone else)
Froggy Boogie
Don't Break the Ice
Bandu / Bausack
Blokus / Blokus Duo
Sequence for Kids
Tiddly Winks
The Ladybug Game
Old Maid
Chinese Checkers
