OK, I've had my iPhone for just a week but it has already transformed my daily train journey. These are the apps I've been using most so far...
National Rail - OK, so it's not cheap but it's worth paying for because it's so much nicer to use on the small screen than the NR website.
The Guardian and Crosswords - seems like an extravagance, but I've not had to buy a daily paper since I've had these two apps, so they've already paid for themselves. Doing a crossword on the small screen isn't quite as satisfying as doing it on paper, and there's no doodling space for working out anagrams, but it's a very neat app none the less. And it gives access to loads of other free crosswords, both cryptic and quick, not just the Guardian.
The Telegraph - not as slick as the Guardian app but it is free. I like to look at the Torygraph occasionally for a change of perspective.
Sky Sports Score Centre - looking up the football scores was one of my main reasons for using online access on my old phone. This does the job sooooo much better.
Units and a2z Pro - both unit conversion apps. I like Units better, with its neat calculator-like interface.
The Good Beer Guide - so much more convenient than lugging the weighty tome around with you. I might have to cancel my subscription to the paper version.
Flixster - movie information, listings, trailers... works brilliantly.
Yell.com - handy and free.
Sky+ - was a slight pain to set up but already proving indispensible.
This American Life - a companion app to one of my favourite podcasts. It gives access to the whole TAL archive, with the option of streaming (free) or downloading (paid) old episodes.
Amazon - neat, functional and free.
Jumsoft Money and PocketMoney Lite - personal financial management. I used to use Quicken on my desktop PC but because it is tied to a single location, I was never very good at keeping it up to date. Hopefully, one of these will overcome that problem - I've not really got to grips with either yet, so I don't know which is best.
Fstream - thanks for the recommendations upthread, folks. This is great. Just a shame you can't listen to radio while using other apps. Why won't Apple do something about making the iPhone's built-in FM capabilities available for this use?
Facebook and TweetDeck - I've never really taken to Facebook or Twitter before now, but social networking makes more sense to me when you have full mobile access.
Byline - nicely packaged interface for Google Reader. Very basic but works well.
Photobucket - makes uploading camphone pics very easy.
ShopShop and My Lists - shopping list managers. Of the two, I think I'll end up using My Lists. It seems quite versatile but I haven't really explored its capabilities fully yet. One of those that will probably become more useful the more you use it.
Assorted games - of which the ones I play most are BeeCells, Flight Control, Doodle Jump and Cogs. Frivolous but a good way to pass a train journey. I don't begrudge paying for games when they individually cost less than a pint and provide more enduring entertainment.
I've also used it as a phone occasionally.
d.