I have a total of four screens including the Apple ones.
Some are there because they might come in handy one day.
Some were impulse buys and have had very little/no use after the initial sequence: Installation - Wow - Why?

The ones I use regularly:

Tweetie - Free - but I'll have a look at TwitterFon now.
Sudoku Unlimited - £1.79. Handy in waiting rooms
Light - Free, Not sure it's still there, it was Erica Sadun's first app. Useful for finding stuff in dark corners; peering at the back of a PC under a desk; dealing with power cuts ...
Remote - Free

Games I occasionally play:

Toy Bot
Super Monkey Ball
Frenzic
Enigmo

MyRail Lite- now RIP in store, PRAY it will come back, the only thing that works to find a train easily.
London Tube- I live in SW and get lost in the tube being a yokel
WiFinder- was on special offer
Remote- Yay!
Shazam- for the wow factor
Nimbuzz- free messaging client AND does voice Skype on wifi better than Fring, very little echo.
Stanza- all those books to read on the plane!
Seismometer- for when in San Francisco 8)
iHandy Level- for when drinking vodka
Units - how many ergs in a gill?
MobileFiles- it works!
Translator- for when brain cells die too fast.

Games & fun
iPint
Hangman
PAC-MAN
SimCIty
Google Earth

Fstream - Free streaming radio app. (have been able to add BBC1-5 Live)
Joost - Streaming Video thingy.. Free has all previous Series of Shameless
Apple Remote - Free
Light - Free (is just a white screen) but great for a light when poking round under and behind stuff ie computers under a desk
Wikipanion - Free iphone compatible Wikipedia
Ihandy level Free spirit level
Around Me or Locly Free - tells you nearest banks, shops, petrol, pubs etc
Shazam - Free - Great for idenitying music you cant identify
Last Fm Free -
Movies - Free - Trailers, upcoming releases and DVDs and local screening times
Air Mouse (£3.50) but worth it gives you a wireless trackpad/keyboard on the phone for your computer especially good if pc linked into TV
Google Earth - Free
Virtual Pool (£0.59) very realistic pool
ifooty - free all the football news by club

Could go on but have deleted and reloaded loads.

In reply to a post by radiomarko:

MyRail Lite- now RIP in store, PRAY it will come back, the only thing that works to find a train easily.

http://themacbox.co.uk/iphone/trains/#_Search works for me.. Just add it as a bookmark/home screen icon.

Also, TubeDeluxe and Movies are awesome.

Edited by xela (Fri 20-Mar-09 19:33:15)

Thanks xela, if MyRail stops working I shall certainly use it.

I have:

Facebook (free, must have for a Facebook user)
Texas HoldEm (£2.99)
Locly (free, uses your GPS coordinates to find local twitters, flickr images, news, local events, pubs, etc)
NYTimes (free, good for news)
Flashlight (free)
Google (free)
Units (free or 59p, can't remember, but useful for conversions)
Banner (59p, displays whatever text you want as a scrolling LED matrix-like display)
iChalky (£1.19, daft chalk-man that dances to music or to iPhone movements)
Line Rider iRide (£1.79, fun iPhone take on the classic Line Rider game)
Wikipanion (free, great for using Wikipedia)
Shakespeare (free, complete works of Shakespeare)
Google Earth (free)
iShoot (£1.79, highly addictive Worms-esque game but with nukes and what not)
TwitterFon (free)
WordPress (free, lets me blog from my iPhone)

Out of all of them I use Facebook and iShoot daily, although I'm starting to use TwitterFon more.

Thanks all.

How damned cool is it that you can have the complete works of Shakespeare on a phone in your pocket?

Must have for me are:
Traffic UK - A slightly esoteric interface but uses a reliable data feed.
Vicinity - Where can I get Pizza?
TimeTracker - I've tried a few Time Tracking apps and this is the best IMHO
BA Flights
Starmap
TwitterFon
BeeJiveIM
XPlane / Sully's Flight
Evernote - Syncs notes with Mac and PC
TouchTerm - SSH client
RDP Lite - RDP Client
Midomi - I find it more reliable than Shazam
Wikipanion

Here's one peeps might find interesting

FixMyStreet

(Just got street light fixed and a pothole filled via these guys)

Amazing. The iPhone is so versatile, thanks to the App store.