A couple people I know have recently acquired iPhones and I’ve been asked a couple times which applications (aka apps from the App Store) I like/use the most. Here’s a list:
I could definitely not live without Twitterific Premium ($3.99), Yelp (free), Facebook for iPhone (free) and NetNewsWire (my RSS reader). This app hooks up with a desktop version which you have to download online at NewsGator.com for free).
Most banks have Mobile software so you can check your balance by logging in from the iPhone. I have Chase Mobile.
PayPal has a good iPhone app that is useful for sending money quickly without having to use a web form.