When talking of short flight numbers, Speedbird 9 is what jumped to mind ... at least for me.

> Ladies and gentlemen, this is your captain speaking. We have a small problem. All four engines have stopped. We are doing our damnedest to get them going again. I trust you are not in too much distress.

British Airways Flight 9, from London Heathrow to Auckland, 24 June 1982.

returns an error on some air canada flights. 8032 doesn't work

Same with some Hawaiian Airlines flights :)