My favorite app changes often! Right now I use "Lose It!" a dozen times a day to track my calorie consumption and exercise.
Some of my other favorite apps of the past are:
1) Angry Birds - physics puzzler where you fight pigs by launching birds from a slingshot.
2) Cut The Rope - another puzzler where you try to get a candy to your pet monster.
3) Conquest - Risk-style strategy game.
4) Air Video - Stream video from your desktop PC or Mac to your iPhone.
5) Air Sharing Pro - read PDFs, jpgs, and watch movies. Also prints.
6) Epic Win - RPG style to-do list manager.
7) Galcon - strategy game.
8) Labyrinth, Labyrinth 2 - rolling puzzle game.
9) Ramp Champ - the best skeeball game! Crazy, funny levels and prizes!
10) Sketchbook - the best drawing app.
11) MorphWiz - the best music improvising app.