I've dallied with numerous train travel focused apps over the years, but settled down with Train Tickets for a long-term relationship. The reason for that is simple – it does a huge amount through a clear, easy to use interface. It is the only train travel app I need.
When you are looking for a train for a particular journey this app will tell you departure and journey times, and even what platform you need to head for. The other handy feature for unfamiliar locations is the ability to locate a station on a map.
If you are collecting someone, then the Live Train Times part of the app is invaluable. It tells you if trains are running on time, and with larger stations knowing a train is arriving at platform 9D can certainly be a boon (though you may have trouble finding the platform itself). I also use this part of the app for checking out departure times for stations I use often as it remembers the last stations searched.
You can also buy tickets through the app for any train journey in Great Britain, and where they are supported you can use m-tickets (handset-only rather than physical tickets).
Product: Train Tickets
OS: Android, iOS, Windows Phone