I must qualify this post by saying that I have an Android, not an iPhone, so there are some awesome games that are not available to me. But here we go:
1. Scramble: This is like Boggle for your phone. I grew up playing Boggle with my grandma, and I still play every time I see her, so this game is nostalgic for me. Plus, since I love Boggle, I am destined to hate Scrabble, so I do not play Words with Friends.
2. Jewels Star: It's essentially Bejeweled for your cell phone. I tend to play this game when I'm waiting for the metro (or while I'm on the metro if I forgot to bring a book or sudoku with me). I like this game because I don't need another player; I can advance as quickly as I want.
3. Text Twist: Another fun word game. I only have the demo version, but it still entertains me, and I usually learn a new word (or rediscover one of those words I haven't seen since I took the SAT) each time I play.
4. Flow Free: My sister introduced me to this game. While fun (and pretty easy) in the beginning, once I reached the harder levels, I sort of gave up. Brain-teasers are only good until the point that they are impossible to figure out. Then I just choose a different game to play.
5. Draw Free: It took me a long time to succumb to this game, so long that by the time I downloaded the app, no one played it anymore. So, as long as you have someone to play with, it's as good as Pictionary. But if you don't have a partner, you can't play. And that's lame.