Originally Posted by
Flying Lawyer
The only notable exception I am aware of in Europe is LHR. In Germany I am not aware of any public transport taking you out of an airport where you don't need to pay.
BHX has a free (albeit short) shuttle train, there's the shuttle bus at FRA that goes between terminals (and the train station), which is free of charge too. There's more examples than just the one. DLR at LCY is a bad example since LCY is just a stop along a regular light rail line - SkyTrain just goes back and forth between the airport and the train station.