I searched but didn't find anything, and i'm surprised there's not already a thread about this. Now that the iPhone is rapidly becoming one of the more successful (profitable) platforms, there are actually some seriously great games out for it. I'm sure people here have some favorites, lets hear em!
I can't say anything about other operating systems (although I hear android is starting to do pretty good), but there's an insane amount of stuff out there now. Some of my favorites for the iphone OS:
Super Quick Hook - 16 bit style retro platformer, feels like it would have been right at home along side Sonic on the Sega. Addicting and seriously challenging, especially the levels that have been recently added by the developer, which are murderously hard. It's 8-bit predecessor, Hook Champ, is also great.
Peggle/Plants vs Zombies - Perfect ports of the pc games. Not much more needs to be said. Almost the exact same content as the computer versions, for a quarter of the price, if that.
Words with Friends - as seen on penny arcade
. Easily the best video game of Scrabble. Able to be played over long periods of times (weeks sometimes), each person taking their turn when they feel like it.
Carcassonne - near perfect adaptation of the board game. Like words, can be played online with people over turns. It looks, feels, and plays beautifully.
Tilt to Live - great tilt/motion controlled game. A little similar to geometry wars, but not really a shooter. You grab weapons that are insta-use, like nukes, or laser beams, to kill the red dots who attempt to destroy you. Frantic and awesome.
Edge - insane isometric platformer/puzzler. Hard to describe, but amazingly well made, and really tough.
Fargoal - Remake of the very very old pc roguelike. Great graphics and controls. It's no Nethack (which there is also a iphone version, albeit not a great port), but it has a surprising amount of depth and challenge.
I could name more, but those are probably my favorite at the moment. How about everyone else?