Some of my favorites are:
Adventure games - Beneath a Steel Sky, Monkey Island and Broken Sword
Rogue Touch - an excellent port of Rogue, without ASCII graphics or clunky control problems
Voice Fantasy - you can summon warriors to fight based on the volume and pitch of your voice. This is a great one to play with friends.
The first Ace Attorney game
Dungeon Scroll - I don't normally like word games, but in this game the words I form kill monsters.
Developers have lately been taking the iDevices more seriously, as can be seen with games like Infinity Blade.