Many moons ago I was, frankly, having an extended domestic argument with the then other half in the airport and lost track of time. United Airlines were very nice about it and put me on the next flight, so I was then obliged to spend more hours with the then other half, the mutual atmosphere didn't improve much...
And one time the Victorian transport system of London suffered a complete breakdown and I got to the checkin at LGW about 59 minutes before departure. Much punching of buttons by the Continental checkin staff still couldn't get me on the flight since it had been closed automaticaly (they probably tried hard because it was the Business checkin, but as we all know BAA's airports' security don't care about service to anyone, premium or not). They considered it to be an involuntary reroute and immediately put me on a different connection a few hours later.
And then more recently I completely f
up the train connections from central Tokyo to Narita and showed up 2 hours after the ANA departure. They were, in the end, not entirely unreasonable about it and slapped me with a GBP200 ticket change fee (on a nonchange nonrefund thought-I-was-doomed ticket) and put me on the next day's flight.
Oh, and then there's the time I misread the departure time as the checkin opening time for an EZY flight and missed it by an hour and some... a few minutes at the service counter and GBP50 later and I was on the later flight.
I expect being very polite helped me out in all cases when it was my fault, but really, if you've made a mistake yourself, go shout at the responsible party in the mirror in a room on your own, not any staff who might help you if they feel inclined...