Here's some things I've used it for:

-- Securing audio recorder to microphone (though I tend to use rubber bands now).
-- Covering cables on floor for safety reasons.
-- Securing microphone stand in weird position to point at soundspeakers.
-- Securing diffusion filter to LED lights (since they sometimes get detached).
-- GoPro attachment.
-- Protective cover for 9V batteries (apparently, there's a chance of explosion if the ends connect).
-- Shoe repair. (Sole came unstuck, so spent the rest of the day with gaffer tape on front of shoe.)
-- Car repair (Numberplate came unbolted.)
-- Headphone repair (to stop ear muffs coming off).
-- Tripod repair (Lever for tilt lock came unbolted.)
-- Spectacles repair.
-- Microphone enhancement (attached to 9V batteries in Rode VMP, to be able to pull them out).
-- Steadicam enhancement (dovetail plate seemed to be a little loose -- solution was gaffer tape in the gap).
-- Securing monopod in weird, cramped position where tripod wouldn't fit.
-- Bag camouflage (for covering up lettering like "Lowepro" to make the bags slightly less conspicuous).
-- Monopod enhancement (attached tripod strap so I could carry monopod around on back... I rigged this together in a café before starting the wedding, and the waitress commented, "Gaffer tape holds the world together.")

Apart from the mandatory taping cables to the venue floor I also have a tiny strip over the battery compartment of my transmitters .. the darn cover kept falling off and hunting for a battery cover in a dark crowded venue isn't really fun at all!!

At lecterns during speeches I also put a piece over my desk stand mic base so it doesn't slip around and then a second strip over the transmitter (one speaker gestured with his hand once and swept the transmitter onto the floor obviously disconnecting it from the mic)

I always keep 2 rolls in my lighting case!

Nice list Adrian!!

I used it on a screaming child once during the ceremony, got some clear audio because of that.
I always have one roll in my gearbag as there always will be an occasion you might need it.

It's even good for a band aid .. I ripped my hand on my old stedicam arm once and there is nothing more inconvenient than trying to shoot when you have blood dripping everywhere! A small folded square of toilet paper (unused) in the middle of a strip of gaffer tape and all was OK ... It was a little painful at home when I had to rip a 2" wide strip of black tape off my skin though!!

always have a roll of tape in a bag, invariably I use it to tape my radio mic to the venue's one, I've only been in one place that my mic can be matched to the hotel's sound system.

On two occasions the groom split his pants prior to the ceremony. Gaff tape to the rescue. On one occasion I split MY pants. Don't ask how but once again, gaff tape to the rescue.
Yes, I've used for the customary taping down cables, holding equipment together, holding mic paks to lecterns, etc but the pants thing is top on my list.

A few of the above on a regular basis. My favourite one so far. I was adjusting a video head that sits on top of my slider the night before a wedding. As soon as I opened the boot to the car at the wedding venue the next day it immediately hit me. I think I left the video head in the office. Sure enough, I had. Had to gaffer the camera to the mount on the slider. Limited me somewhat on the day but got away with it. Had to drag around 2 tripods most of the time. One for general shots and then swap over for a slide shot when required.

Was hired to cover a wedding ceremony inside a huge geodesic glass dome (botanical garden). Plenty of light coming in right? Sure, except they ran late and it got dark out very quickly. The couple was going to stand inside a gazebo thing with the minister. I grabbed my on-camera LED light and duct-taped it up inside the doorway of the gazebo aiming down at the couple and minister. Out of sight of guests.

This not only provided me with great lighting for the video recording, but the guests would not have seen much without it either, as it got very dark and there was NO lighting in the dome at all. The photographer was also very thankful as he would not have been able to focus without the light. There was no other way to attach the light other than tape.

Thanks