My favourites are Oceanhorn and The Bard´s tale, and some point´n click-games, like the original Monkey Island games, though I seem to get back to The battle for wesnoth again and again, works just as well on the iPad as it does for linux.
I like fantasy/adventure-games mostly.
Action/racing doesn´t do it for me on the iPad. Strategy-games works out rather well, but when in realtime they get a bit annoying, since the lack of shortcuts and stuff makes you too slow.
RPG like Ravensword, works in a way, but I mostly felt it was annoying, was thinking that it would be better on a computer, all the time, a bit the same way action-games needs keyboard and mouse. Got a keyboard for my pad, but no games I´ve found are making the use of it yet. 
And the Infinity Blade series, I find it too repetitive and constricted. Played through them twice, got annoyed, deleted. I´d like to see a real fantasy-game using the Unreal engine.
Some games that I consider great:
•Temple Run and all games like it
•Tiny wings
•Flappy Bird
•And - I’m surprised nobody mentioned this - 2048.
Some of my favs. :
- BADLAND
- trainyard
- icebreaker
- Kingdom rush frontiers
- Rayman fiesta run
well iPad games would be: Infinity blade (love the UDK), Smash, Galaxy on Fire series, Ascendancy, and Imperium Galactica 2! (just got android release as well :D)
Definitely on PC and other things would be: Portal, Halflife series, Unreal Tournament…and the original ELITE (freaking awesome game, best version is NES)
2048 and geometry dash both awesome games