I've had a series of minor glitches, but my absolute biggest fuckup was the one that DIDN'T happen.

Before going back to college in my early 20s, I was, for a short period of time, a "ramp rat" for a major airline. Part of the duties of ramp personnel are to operate the pushback tractor, or "tug" (this was at a smaller airport, so we never had widebody aircraft- the biggest we had were 737s and an assortment of regional jets. Our tugs were a good bit smaller than the huge ones you see pushing 747s.)

One morning before dawn, I was to push back the first flight of the day. Being relatively new to the job (this was only my second or third unsupervised pushback) I hadn't quite gotten the "feel" for a particular parking spot, which sat at an awkward angle at the end of the smallish terminal. So...secure the tow bar, make sure wingwalker is in position, talk to the crew over the intercom, start the pushback...

At this particular airport, it's necessary to push the aircraft back for about seven or eight seconds, then start a sharp turn to get the aircraft in position to get out to the taxiway. My wingwalker waved his light stick to indicate when to start my turn...and never stopped indicating the turn. After a couple seconds I thought, "we should be straightening out by now," and slowed to a halt (remember, 90% of what I can see is the nose of the airplane I'm pushing.) He was just out for a morning stroll, forgetting completely to stop waving his light stick (the signal for a turn.)

I had stopped about ten feet or so from pushing the tail of a 737 into the tail of another airline's MD-80 at the adjacent gate. The wings of the aircraft were, uh, pretty damned close as well. My wingwalker wasn't even paying attention- he just was strolling along without actually looking at his surroundings. I VERY carefully extracted the 737 from its awkward spot, exchanged pleasantries with the crew (who, if they noticed anything amiss, didn't say anything) disconnected the towbar, and went on my merry way.

Afterwards, I very calmly explained to the wingwalker to please fucking SIGNAL me next time I'm about to hit a plane with the one I'm pushing. He was fired not long after that for something unrelated (I never found out what) and I found a better job elsewhere that was more compatible with a class schedule.

TL;DR- My biggest professional fuckup wasn't one, in the end, but nearly heavily damaged two airliners from two different airlines.