Right when you get your iphone, you'll probably end up downloading a shitload of apps and deleting most of them later. The ones I still regularly use:
New York Times - Obvious, but this is probably the thing I look at most on the bus.
Shazam - You're at the mall. You need to know what you're listening to at the shoe store.
White Noise - If you need noise to sleep, this is essential
Weather Channel - Works way better than the built-in weater app.
ebay
Urbanspoon (for finding restaurants in the area, not sure how many cities it works in)
Drinks (mixed drink recipes, useful if you only have random shit in the cabinet)
Flixter (best app for looking up movie times with a summary of reviews - very helpful if you just saw a movie and are contemplating sneaking into a second one)
IMDB (internet movie database - apparently there's a deluxe one but I dunno what it does)
What's On (best app for looking up tv times & seeing when Law & Order is on next - can be used with whatever cable/antenna you have)
Guitar Tuner
Routesy bus times
Sportaculuar sports scores, schedules, etc.
Myphone lets you link all your phone contacts with fbook so you automatically have photos come up when people call you, if you're into that sort of thing
This American Life (new app is really amazing, has every episode, and now you can save them if you're heading into spotty reception)
Simplify - I don't actually use this one much, but I still think it's pretty great to be able to access your home itunes from your work or phone.
Pandora - I don't really need this either but it can be pretty handy if you're driving and get sick of whatever you've got.
WunderRadio - Reallly good internet radio app, I use it mainly for listening to NPR in the morning - it works better than the NPR app.
Dropbox - I don't actually use this all that much either but I think the whole concept of Dropbox rules, being able to automatically have files at home, work & phone instantly...
Tipstar - yes, this comes in handy when your friends try to skimp out
Goodreader - If you download a book as a big pdf, you can read them on your phone.
By the way, that new Netflix app just blew my mind!!!