On iPhone, try the Tube Tamer app: https://itunes.apple.com/gb/app/tube...558106521?mt=8

This uses the same data as the TfL journey planner, so it takes into account line closures, engineering work, etc. Very easy and quick to use. There's probably something similar for Android, too. Unfortunately it only works for Greater London and around.

Other than Google Maps and the TransportDirect site that Stut mentioned (both of which have their limitations), there isn't really a good transport planner app/site that works throughout the UK, yet.