Specifically, something that feels like an actual game, and not a lot of the garbage timewasters that somehow become popular on the iOS store.
As an example of a real-time game, I quite enjoyed 10000000, having heard it get a recommendation on the 8-4 podcast.
And as an example of a turn-based game, Hero Academy is surprisingly well balanced and I can actually manage to keep a pretty decent win rate going.
I appreciated what Sword & Sworcery was trying to do, but fuck the writing in that game; there's a way to be self aware without coming off as a snarky asshole who thinks they're so fucking clever. And I've played the first Infinity Blade a fair amount and enjoyed it, though it becomes evident pretty quickly how little content there is in the game, plus it burns through battery like there's no tomorrow.
And I'm pretty much not interested in anything that remotely resembles Tiny Tower, Pocket Planes, etc. I guess I'm alright with endless games like Canabalt or Jetpack Joyride, though they do straddle that line of "legitimately fun Flash-style game" vs. "pointless timewaster that goes nowhere".