Avernum: Escape From the Pit, Infinity Blade, King of Dragon Pass, and Jetpack Joyride--these are but a few of the games I have downloaded onto my new iPad.
I've spent the most time so far with Infinity Blade--enough time to make my wrist hurt the next day. It's a pretty great game; it looks very nice, and it has a solid, if simple, set of mechanics with a hook that keeps you coming back. The one area it fails in is the menu system. It looks completely amateurish next to the best-in-class graphics that the rest of the game sport. It's baffling how awful the menus look; I wonder what the story was, there?
Avernum is probably the game I am most excited about digging more into on the tablet. It's a redux of an old Mac RPG by Spiderweb Software, and probably compares most easily to something like Fallout or Baldur's Gate. Though combat is turn-based, like the former, you control a party of archetypical fantasy character classes like the latter. Supposedly it's three games in one; there are three distinctly different ways to progress through to the end and complete the game. This is the type of thing I can really sink my teeth into, on a platform more often characterized by its casual fare.
King of Dragon Pass is another hardcore game for the tablet. Perhaps too hardcore. The closest thing I can approximate it to would be one of Paradox's grand strategy games like Europa Universalis or Sengoku, only you don't dwell too much on the map screen, from what I can tell. You play the leader of a tribe just immigrating into the realm of Dragon Pass, and must make all sorts of decisions about how to budget, what crops to plant, what gods to sacrifice to, who to raid, how many warriors to keep around and how many should go back to being farmers. It's turn based, with each turn being a season, as far as I can tell. Events will pop up here and there and you have to decide how to deal with them and how that might affect the diplomatic situation with neighboring tribes. There's a big element of calling in favors with other tribal leaders out there, as well as giving the gift of a few head of cattle or men-at-arms. I've never been one to dig too deep on a game like this (Civ V is about as far as I've gotten), but I do want to keep at it here and there if for no other reason than to roleplay as a tribal leader.
Jetpack Joyride is a pretty simple game in the mold of Canabalt, where you control a guy wearing a jetpack as he flies across the screen to the right. By touching the screen you apply propulsion, sending the guy up and down as you modulate how long your burns are. There are hazards to avoid, and things to collect, and it's just interesting enough to keep you happy for a few minutes at a time. In other words, it's a great way to waste 5 or 10 minutes, like a lot of iOS games.