Was once delayed as a passenger due to extreme cold weather. The cold weather resulted in a frozen fuel pump on the fuel truck, which had to be defrosted using a forced air heater. When the truck drove away, it drove over the electrical umbilical to the turboprop, which was severed. Finally got cleared for boarding (the now dark/unpowered/unheated aircraft). After walking across the ramp in -30 degree weather, the lady at the front of the line tripped walking up the stairs and dumped her purse into the lav/entryway of the aircraft. We finally get onboard (FA screaming "just sit anywhere so we can close the door!") and the ground crew comes out to deice the plane... the pump deice truck is frozen too and they can't get more than a trickle (think kinked garden hose) to "spray" out of the nozzle. The crew ended up defrosting us with a bucket and floor mop. Finally get started and cleared to the end of the runway and we end head to head on the taxiway with another aircraft that made a wrong turn. Ground ops had to come out with tug to push him back 100' so we could get to the next turnoff.
Other delays: Flight cancelled due to the door on the CRJ falling completely off the aircraft after being hit very forcefully by a jetbridge.
Delayed due to an FAA inspector grounding the aircraft because the tread on the door of the CRJ "Didn't have enough grit to prevent somebody from slipping when the door got wet". The weather that day was clear and a million with no chance of rain insight.
Delayed once due to an FAA inspector that demanded to "ride along" at the cost of bumping three passengers due to weight and balance issues. He ended up getting left behind after we figured out he was a GA inspector from a FSDO that wasn't anywhere close to our geographic area of operations.
Delayed once in CMH to wait for lifeguard medical materials. Ended up being King Cobra snakebite anti-venom from Jack Henna's zoo.
Fly long enough and you'll see all sorts of oddball stuff happen...