I always preferred short games, that you way could play a couple games in not much time. That eliminates Chutes and Ladders and Candy Land for me. As a busy parent, I rarely had time to play such long games.
Give me a few rounds of Hi Ho Cherry Oh and I was good to go. Also, if your three year old can count to 10 and recognize numbers to ten, Skip-Bo is another good one- it can be as long or as short of a game as you want it to be.