I just got a new iPhone, too. I started a thread in IMHO soliciting good free iPhone apps. I’ll quote myself and give you some of my favorites.
Some more cool ones are:
I Retro Phone, which puts an old-fashioned rotary phone dial on your home screen. It actually works. Put your finger in the appropriate hole, drag it to the stop, and watch as it returns the dial back to position, with realistic sounds. Couple that with the bell ringtone in your iPhone, and you can be totally retro. You can even type your own phone number into the little sticker in the center of the dial. It’s only 99 cents for a limited time.
Stanza is a free e-book application with a library of free books for download.
Amazon also has a Kindle reader. The application is free. Amazon has a library of free books for download, but you can also purchase books from Amazon if you desire.
Lots of other good applications in the other thread, too.