I haven't even come close to trying out all the app games I want to try, but here are some of my list of favorite app games in no particular order:
Angry Birds and the various versions of this franchise - Loved it when it first came out and still love it through Angry Birds Space. Hope they can keep this franchise going but yet keep it fun to play.
Doodle Jump - A cool but simple game. I've played games that look so incredibly real on the regular game consoles, but this one is great in the design looks like it was just drawn up buy a child.
Temple Run - Kind of like the Indiana Jones movies in the game design and play.
Cave Bowling - Who knew of cave men bowled - but this is another one of the many games where you have to hit some object while dealing with the physics of the location the player is in. Enough different screens keeps the gameplay interesting.