Even since I bought my iPhone 4, I've been looking for Apps and Games that run smoothly on it and iOS 4.
Words With Friends, by Newtoy Inc., is a Scrabble-like game that lets you play online against your friends or a random person from around the world. The game just looks great on my Retina display and runs very smoothly.
The game is almost exactly like Scrabble, you get an amount of letter that have a different amount of points each, and you receive a total score depending on the combination you use. You place them on the board a little like a crossword puzzle because you have to attach the letters you use, to the letters already on the board.
Words For Friends allows you to play up to 20 games at a time. You can enable push notifications to pop up every time your opponent makes a move. This makes thing much easier and faster on both ends. If the other player is lagging, tell him to "hurry up" in the implemented chat room.
The great thing about this game is that there is a fully functional free version that just has ads annoying you a little.
Words For Friends Free - Free: iTunes Link
Words For Friends - $1.99: iTunes Link