I love Angry Birds, and am proud to say I have 3 stars on every level
Words With Friends is great, but since my brother doesn't like it that much I don't have anyone to play with (random games suck).
Recently got addicted to Fruit Ninja. The arcade mode is so fun in short bursts!
Here are the other games I have on my iPhone:
Flight Control (this is a classic as well)
Bejeweled 2 (no explanation necessary)
Pinball HD (very good pinball game)
Mahjong (basic pick up and play)
Osmos (loved the PC version, bought it for the atmosphere)
Scramble (like Boggle)
Dungeon Hunter 2 (Diablo clone)
Cut the Rope (has that Angry Birds fun factor)
Plants vs Zombies (you know what it is)
Infinity Blade (Unreal Engine 3 on iOS - eye-popping)
If anybody wants to play anything, my Game Center name is Bube7.