I don't have an iPhone - but I do have an Android phone and most of the 'Official' apps cross over. So, here's some apps that I have or have used:
Flixster / Movieshttp://www.flixster.com/mobile/appsI imagine the iPhone version works the same as the Android, but you can log in with your Facebook account and see all the latest movie showtimes, trailers, what's on near you, etc. You can rate the movies, see pictures, actor info, your friends ratings (based on Facebook friends) and everything. Excellent app for the movie buff!
Brightkitehttp://brightkite.com/Some people have this funny thing about location data - that they don't want people to know where they are. They're quite happy to post a status on Facebook or Twitter saying 'I'm in the Lake District. It's sunny here.', but then if there's a status which says 'I'm in the Lake District. It's sunny here. - [link to a map]' they freak out because people know you're not at home! No shit.
Anyway, if you're into location based updates, that's what Brightkite does. It will link your status updates to where you are in the world. You can also upload photos too! It syncs with Twitter, Facebook and Flickr too. Nice.
Foursquarehttp://foursquare.com/Another location-based app, but this time a game. You basically 'check in' at locations and every so often you'll get rewards (ie, visit a place three times and you become a 'local'). If you visit a place more than any other user, you become the Mayor of that place - but can have that stripped if someone is more of a regular than you are to that haunt. Syncs with Twitter.
Last.fmhttp://www.last.fm/hardware/appleSocial music service Last.fm have an app that lets you stream and scrobble. Or at least, on Android it does.
Facebookhttp://www.facebook.com/iphoneEnough said.
Meebo IMhttp://www.meebo.com/iphone/Instant messaging on-the-go. It supports a wide array of accounts and you can sign into them individually, or create a Meebo account and link them altogether for a one-click sign in process.
Edit: Apparently
Trillian is better than Meebo on the iPhone, says
@dustinwilson - a man to be trusted!
ShopSavvyhttp://www.biggu.com/apps/shopsavvy-iphone/Scan in the barcode of an item to find reviews of that product and also prices from online stores and shops local to your location. Money saving app, made of win.