Here are my recommendations for iPad games:
I'm not mentioning the Angry Birds/Cut the Rope/World of Goo/Flight Control type games, because if you haven't come across them maybe you need to do a bit of googleing!
Reckless Racing HD
This is often my go-to game if I need a quick adrenaline fix. The controls can take some time to get used to, but it is well worth the wait. A great feature is you can play against friends on other iOS devices.
Osmos for iPad
The most beautiful app I have seen. Although you can get this app on the Mac App Store it rightly belongs on the iPad because of the interface and intimacy of the device. The music is very absorbing, with a string ambient theme that needs to be appreciated with headphones in a dimly lit room.
Bike Baron
A fun physics based motorbike game where you have to guide the Baron's bike over increasingly complicated courses. Comical, cheap and mildly addictive. You can even download levels or make them yourself.
Mirror's Edge
Originally a PC and console game, Mirror's Edge was re-coded for the iPad and shows that the platform can perform like a dedicated gaming platform. The controls can get irritating at times, but it is lovely to look at and fun to play if you get in the rhythm of it.
