Most interesting delay as a pax: Was delayed last year [MENTION=784783]ATL[/MENTION] while the FNT airport was closed after one of the airport policemen were stabbed. Thankfully the cop was ok.
But I have a bunch from my time in the biz.
As a ramp supv at UA: One we had a delay because one of the ramp crew's hats got sucked into the APU intake (on the bottom of an A320) while he was removing the main gear chocks. Had to wait for MX to come remove the hat. Took a 5 min delay, which irked me because I had to then write a delay report...and the flight still arrived early.
Also had a ramper doing a walkaround during pushback who noticed something strange near where the pax door was connected to a jetway. MX was called to check it out, and it turns out it was bubblegum. Took a 7 min delay, and then I fought with ops to have it coded as a miscellaneous delay, as opposed to a ramp delay. Eventually I won the argument.
Once had a ramper loading a 777 for the TATL flight point out that a kennel that was too small for the dog. A discussion between myself (ramp supv) and a CS supv ensued and we agreed that it was in fact too small. There are rules about the dog has to be able to stand up and turn around, etc. etc. Anyway, this was only 10 or so minutes before departure (dogs are loaded last into the bulk pit of 777s). So we checked with everyone inside UA that might have a kennel, and we got lucky that cargo had one that was big enough. So we sent a ramper to go get it. It's a long trek to the cargo area and back and by the time everything was sorted, we took a 20 minute delay. Ops also tried to stick that one to the ramp, but I got it (properly) coded to CS, since they never should have accepted the dog at check in. Put a nice letter in the ramper's file for doing the right thing and reporting it. With recent events it may be hard to believe that UA actually cared about a dog.
As a gate agent I was once working an AC flight. There was a group of extremely large women that were together and the airplane didn't have enough seat belt extensions. We also didn't have any AC extensions in our office (UA ground handled their flights). Apparently UA and AC seat belt extensions are not compatible (lesson learned). So I had to go to other airlines to see if I could find some. Thankfully WN had a bunch that were compatible and let us "borrow" them. Took a 25 minute delay that I did get stuck with. Oh well. It was not a comfortable situation for any of us!
There are probably hundreds of other stories. Once I was deicing a RON aircraft with a half inch of ice all over it. Ran out of Glycol, went to the Glycol farm, and all the pumps were frozen with the ice covering and wouldn't work. Had to cancel the flight. Thankfully this one was just a re-position for a charter. We'd already cancelled all the other RONs the night before due to the ice storm.