There are a few iPhone games I often play. One is Doodle Jump.
I classify DJ as a jump game, a game where you steer a jumping character. The Doodle has what it takes to become a star in the app world. It's cute. It's also important that the steering feels good. I always accept that the death of the Doodle is entirely my own fault and that's a strong indication that the game is fair and the steering is good. This is a very important characteristic of all games.
Further, the sounds are excellent, which is important. Things sound as you would expect them to in this game. The monsters are a laugh and they seem to be saying "very wrong, very wrong".
My kids like to use the different scenes, like the jungle or the football pitch or the Dracula. I don't and I only use them when my kids insist I do. Sadly I'm not a skilled Doodle player. My 6-year old boy's high-score is more than 3 times my own.
I haven't played the game in multi-player mode yet. That's probably because I'm not skilled enough. I need to practice.