Are you going to jailbreak your iPhone? I highly recommend it.
Here are a list of my commonly used apps for a non-jailbroken iPhone:
Beejive IM - as good as it gets for mobile IMing. If you do this a lot it's worth the price.
iShoot Lite - Very fun, considering upgrading to the full version.
Ocarina - So. Cool.
Fieldrunners - Was fun for quite some time, but limited in depth.
Pandora - One of my favorite apps. Streaming music to your iPhone. Sweet.
Sportstap - Not as good as Sportacular, but the latter won't run after jailbreak (v 2.1)
Remote - Lots of fun, and actually handy if you have a PC set up in your house with good speakers.
Shazam - Awesome app. Just awesome.
Backgrounds - Sweet BGs for the iPhone.
Easy Relax - A VERY cool relaxation program that's quite customizable. Want a fireplace with a flute? Easy. Want a rainstorm with drums? That's possible, too. I always use this if I'm not in my own bed, as it's soothing to listen to when you're in an unfamiliar place.