There are so many types of games, they just run the gamut. Fortunately a good many are free, or start out free so you can try them without really losing anything. I like to check the "new and noteworthy" section @ iTunes for new additions.
So, to answer your question directly: I love Plants Vs. Zombies. My son is addicted to Army of Darkness. Then there's the Angry Birds genre, of course. Cut the Rope is similar to that, cute and fun. I have something like 75 or 80 games on my iPad that get regular play... you just need to shop around to see what you like.