I'd take the original Diablo in a heartbeat. Know Diablo III would be out of the question. But there's few hack-n-slash games on the iOS on the level of Diablo.
A full version of Monster Hunter Freedom Frontier or Unite with full online multiplayer and I'll be satisfied for a very long time. Phantasy Star Online would also be very welcoming...
Black & White by Peter Mol...ml..molysxn. Think that game would work really well on an iPad. Thief 1 & 2 would be pretty cool too.
For your TF2 cravings get Warm Gun (There's been a LOT of significant updates since its official release, so ignore the negative reviews you'll see around about it's bad performance-it currently runs smooth as butter), for Happy Wheels, Bike Baron will have to suffice.
I would second Phantasy Star Online. Also, more dungeon crawler type games: Champions of Norath X-Men Legends 1/2 Ultimate Alliance Others: Freelancer Dungeon Keeper Team Fortress Classic Mega Man Legends Freedom Force I'll stop for now.
Mario Kart Any version!! It is still imo, one of the most perfect games for the IOS. [you can use joystick or the gyroscope! you can use a simple 1-2 buttom for items/switch]. Or if we are talking games like mario, donkey kong country etc come to mind as well.
Black Lodge 2600, Fez, Rez HD, and Bit.Trip.Runner http://jack.worlord.com/blacklodge2600/ http://polytroncorporation.com/ http://m.ign.com/games/963109 http://bittripgame.com/bittrip-runner.html
Final Fantasy VII/VIII, Disgaea, Castlevania: SOTN, Cave Story, Warcraft III... well there's a lot. But Nintendo's games are never coming to the iOS, so don't waste your hopes naming games like Mario, Zelda, Kirby or Pokemon...