If you want a train in Great Britain, this is the site to plan your journey with. For much of Europe, those clever Germans have it taped. The Swiss chaps have their own timetable site as well. Click the link and choose a station, and you'll get real time departure information. I recommend choosing Darlington, lovely place.
Trains are all very well, but what about other forms of public transport.
Well, there are journey planners that do that. Here's a good one for Cumbria. Mr Slevin at Buckinghamshire, he knows about information. Pick his brains at the Bucks and Milton Keynes site here. Evrything from journey planning to car park spaces.