Well, the most remarkable thing ever to happen to me wasn't with BA. I was flying with a small (but not that small) commuter airline. As I reached the bottom of the steps, I was greeted with "Good morning, Mr Ringbark." It wasn't till I reached my seat that I realised that there was no possible way she could have read my boarding pass or anything else with my name on it...
I knew I flew that route quite a bit, but still...