• BA
• FT
• London Tube Status (there are many, my preferred one is by 'Pete C')
• Skyscanner (useful for pub discussions on why LCCs do not cost less)
• FlightTrack* (I've just noticed this has a Live Wallpaper option which displays either the flights you have tracked or flights from a particular airport)

* paid-for version

I use the trains a great deal but refuse to pay for their app. Their website is a travesty so I doubt very much the app would be much better.