This is a short list of some of my favourite games, which I have yet to remove from my device. So if you don't have any of these then I would highly recommend them. (They are in no particular order)

Field Runners	The first tower defense game I got. Doesn't have as many levels as some others, but the gameplay is still very fun and addictive.
Enigmo	A great puzzle game, with many built in levels, as well as a great number of downloadable levels from other players.
Edge	This is a very unique and fun game, with a good number of levels to keep you playing.
Sway	Another very unique game, where you control each hand of your character to swing your way to the end.
The Creeps!	Another very good tower defense game. It has nice graphics and is very fun, with various different game modes and many levels.
Pocket God	This is a great pick-up-and-play game, with several different mini games to keep you occupied. Has a large number of different ways of interacting with the Pygmy's.
iBlast Moki	This is a very fun and addictive puzzle game, with a built in level editor to keep you playing for even longer.
Mini Squadron	This is a great pick-up-and-play game, with local multiplayer and many different planes to try out.
Doodle Jump	A very simply but addictive game that will keep you playing for a long time.
Flight Control	One of my favourite line drawing games. Has been updated quite a bit, and has lots of really good features.
Angry Birds	A very fun game with a very large number of levels and lots of replay value.