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TweetDeck - Twitter
WeatherBug - Weather
Dictionary.com (not a web-app) - Dictionary & Thesaurus
FlickIt - Flickr
Photoshop.com Mobile (not a web-app) - Image Editing
Opinionaided - Great app if you need an opinion on something
 
Facebook - best facebook app on any mobile device.
Twitter- not the best, but it gets the job done
MobiTV- yea it's pricey but I watched world cup stuck in traffic cos of this
Pandora - with background support, it finally became useful
Hipstamatic - really cool photography app
Pulse mini - I got it on my iPad, and wondered if its gonna be any good on the iphone but it's still amazing on the iPhone too!
Pixelpipe- until apple comes with a solution to upload hd quality, I'll be using this.
Flixster- great for getting movie times etc...
 
Favorite Apps

The apps I use more than once:

TWC
Chase Bank - deposit checks by taking a picture of it - Seriously!
Fandango
The Onion
Google - Voice Search actually works
Facebook
Mass Text Message - send text messages to groups (it's my app, so i'm biased, but it saves me so much time!)
ESPN
The New York Times
Words with Friends
 
Let's get this going again

With over 300,000 apps it's hard to discover all the awesomeness that's out there.

Here a few of my faves.
Iheartradio- awesome radio app

Runkeeper- plots your route, time, speed and distance while biking and running using the gps.

Dictionary- you know what that is

Thesaurus- you know that too

Imdb- facts, info, and goofs about movies
 
BillMinder
Osfoora - Twitter client
BofA
ING Direct
WhatsApp - free texting between my gf and I.
Pandora
TWC
Words with Friend's
Open Table - I love being out with my gf and we can get a reservation on the go.
 
Some New Apps to Try

Ok..

So it looks like this thread has done well so far, but I agree.. we need to keep putting the recommended apps out there.. so keep em coming. I'm going to weigh in on a few that I've tried out lately: (All Free)

CycleTracks - Awesome app for using GPS to track your time/speed and route for biking. Uses a route overlay on Maps and saves the route for future comparison.

MorseMaster - I'm sure many have wondered.. A great app that allows you to type out what you want your IP4's flash to communicate via Morse Code. For all the Lost people out there.

Physics (Or TouchPhysics)
- A really cool puzzle game where you manipulate pieces to complete the puzzle. Good graphics/sound and 200+ puzzles all free.

Speedtest - To check your network upload and download speed.

5-0 Radio
- For all the cops and criminals out there to listen to the local cop speak via scanner.

Redfin
- Great real estate app for certain areas of the country (using it for East coast)

Bambuser - Host a webcam with your iPhone. Seems to be faster than Qik and Ustream Broadcaster

Animation
- Make a cartoon while your bored.


That's all for now.. I'll try more and post as I do.
 
thanks for all the great recs! i love this thread!

awesome note - love the UI, power, flexibility of this to-do, note-taker, and journal.

high school hero - very addicted to this really fun game.

momento - nice journal that automatically includes my tweets

rest & relax - helps me fall asleep every night, despite the creepy icon

hot potato - like twitter but more fun (and automatically connects to twitter too)

mailtones - assigns different notifications for different people who send me emails

myphone+ - automatically syncs my contacts w/ their current fb profile pics

imovie - amazing how well the movies i make on this app turns out. even easier to use than the real thing

streamfree - my favorite sounds to sleep to

nike training - provides workouts, workout schedules, and let me invite my friends so we can challenge each other

water - helps me drink 8 glasses a day and keeps track of my water consumption

ambiance - my favorite alarm clock app

cutiary - cutest app

atomic lite - favorite (fastest) web browser

wordpress - blog from my phone, including pictures

favorite games - bejeweled 2, solitare, tetris, sally's salon, runway, diner dash, traffic rush, mad libs, jailbreaker, doodlejump, oregon trail,
 
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