Okay, I'm adding a few apps to my phone, but I'm struggling to think of useful ones (ie, things other than games). So far I have:

Advanced Task Killer Free - to kill unwanted items from draining the battery
Facebook - for accessing Facebook easily
YouTube - for accessing Youtube easily
Exchanger - live currency conversion
Google Maps - already built into the phone
BeebPlayer - unofficial iPlayer for mobiles

I've removed the wikipedia one as it was pants.
What else do you think I'll find useful
I have an android phone, but feel free to list any type of app for other phones. I'm sure there'll be an equivalent available. I don't need the Flicr or Tweet ones.

These are the ones that are most important for me on my BB:
Buddyguard -useful when phone is lost, included remote lock and wipe
Tubebuddy London Underground and DLR service updates and Tube Live Departure Boards
Tube Map also has live service updates
Train times
Quickpull No, not for birds!! Believe it or not to reboot a BB you need an app (or physically remove the battery).
Bloomberg Mobile to monitor fin. instruments and news
Poynt to find people, businesses, movie theatres, retailers and restaurants depending on my GPS location.
ScoreMobile up-to-the-minute sports scores, boxscores, player stats, betting odds, game previews, recaps, top stories, and league standings.

FreeviewHD - TV Guide for Freeview. You can search for programs, re-order the channels and hide the ones you don't like.

Whatever the Android version of Redlaser is called. A barcode scanner that compares shop prices with internet prices.

Some sort of remote for your computer is a must!

If uRemote is available I'd highly recommend it!

The Skype app is very good on the iPhone, there is bound to be an Android version.

I also like the Amazon.co.uk one.

I've got a few photography ones like Dofmaster, but not useful for anyone but photographers.

Evernote is a must. I link mine to JotNote that allows me to convert a photo of a document into black/white page of text for Evernote to read. JotNote corrects for parallax errors too if you have to take the photo of the document at an slight angle.

I use "Allowance" it gives quick access to the O2 information on how many texts and minutes I have left this month. There has to be an Android app that does the same I would have thought.

As I am on a lean tarrif I find this app pretty useful.

Oh, the MetOffice weather app...

Thanks for the ideas. I don't use all my minutes so I don't need Skype. I can already get a text from Vodafone about my usage. Weather is build into the phone. I looked at the barcode reader, but wasn't convinced the ones on offer.
I'll look into the amazon one as I use that a lot.

I use o2's app for that. It is free after all.

Absolutely, but came out long after I had bought an iPhone and had stumped up my 50p for Allowance.