My favorite games are:
Tapfish - create colorful tankfuls of various fish, grow them then sell them for profit, and breed them to get unique hybrids - absolutely addictive.
Froggy Jump - A very silly jumping game. I'm not sure what the point is but I keep going back to make him jump higher.
250+ Solitaire Collection - This really has over 250 variations of Solitaire and is extremely well done, with demonstrations and next moves for every game.
I also like Angry Birds. Talking Tom is hilarious but I wouldn't call it a game, since you aren't competing or trying to score points.