You can't port Quake to phones, but Gameboy had much worse screen and there were games. Unlike Gameboy, phones have no buttons, but lots of genres don't need fast action and precise pointing. Power consumption might be more serious issue, but some games are okay to redraw screen only on user actions. So it's mostly cultural and market issues.

I really liked Device 6. It’s mostly text-based but takes advantage of some of the phone’s capabilities too. The plot is clever too.

I've found that the touch screen is a near perfect input device for chess. I prefer it to over-the-board play.

I know its silly to say, but I feel like I have much less patience when playing on a touchscreen. It feels much harder to think about the geometry of moves in that way.

That said, I don't think this is the same for everyone, just my observation.

I find the same for Scrabble and Monopoly, though on an iPad rather than a phone. The old version of the Scrabble app used to let you put an iPad on the table for everybody to see, then use the iPhone/iPod as your personal letter rack so people couldn't see each others' letters.