There are so many - try the free ones first. As I said last night I love the daft games - there is one that's like one of those machines at the seaside where you put pennies in and try to get other pennies to fall off a shelf (I have actually shaken my phone to try and get them to fall off!). I've got a spirit level (like I'm ever going to use one of them), if your a member of the National Trust there's one to find their properties, there's loads of stuff for kids (of all ages). If you find any good ones let me know!
I find it very usefull to read the reviews. Apps are quite personal but here are a few of mine:
pocket universe ( point phone at night sky and see what the constellations are and where the planets are)
met office. Good free weather app.
RAC traffic. Very good up to date traffic info.
Radio box. If you have an iPod dock this turns your phone into a digital radio via wi fi.
Husband downloaded that for the kids - you can get one that will allow you to bump your I phone against someone elses and you can share stuff (don't know what stuff - was only half listening).
Don't know about radio apps but thought I would let you know that they do run out of battery quite quickly when you are mucking about playing games, etc but they charge really quickly too. (And they get really filthy if you let the kids play with them!)
ebuddy
myconvert (converts anything)
argos
unblock me (good puzzle game)
sudoku
amazon kindle reader
facegoolite
on this day
fluid
acura free (tells you how much battery you have left)
find my car
national trust
ATM uk
Some good tips for saving battery life: only have it check for email every hour instead of constantly. Don't leave it charging when it's up to 100%. Switch it off overnight especiAlly if your in a weak signal area. Turn the percentage battery life indicator on rather than the silly three bar standard one.
When my husband got me mine I kept saying 'oh, I'll never use it' but I would be lost with out it now - it is just like a mini-laptop (but with really really small writing).