British Airways has recently started accepting iPhone boarding passes. All you have to do is make sure that you have the latest BA iPhone app. You can then use the app (or the Web) to check-in online and have your boarding pass downloaded to your iPhone.
On the iPhone, you will find the boarding passes listed under each flight itinerary. Open up the pass and you will see a small stamp-shaped barcode that can be read by the ground crew when boarding the flight.
At present, iPhone boarding passes are available for all European flights originating from the UK and all UK domestic flights.
Click here to go to the ITunes store.