Great topic, what I find interesting is how people discover those glitches. Sometimes it's pure luck while playing casually, or by forcing luck a little by doing weird stuff. And sometimes it's by actively looking for a glitch, having some hints that something weird will probably happen in some circumstances.
Let's see, what did I discover...
I think the biggest is clipping through the floor with the "pipe machines" in Sonic Advance. (here:
https://youtu.be/4tv5gyAlkRs?t=740).
When you think about it, it's just the application of an already known glitch, but in a place where it has not been done before (it was already present in other runs, using another level device, here:
https://youtu.be/4tv5gyAlkRs?t=286).
The funny part is that I wasn't trying to apply the known glitch elsewhere to find that one, I was "just playing" with the collision of the pipe thing hoping to enter it maybe a frame sooner, with a jump or something else... And the glitch happened ^^.
Another one in Sonic Advance, but it's more like an exploit.
With Amy you have a "whirlwind attack" in the air, which happens to instantly reset the horizontal speed to zero. By using it quickly after hitting a diagonal bumper, you can use it to cancel the horizontal push and only gain height. It was used to take very useful shortcuts (a good example, and where I did the discovery:
https://youtu.be/4tv5gyAlkRs?t=711).
This one I was actively looking for it, or in other words, I did think about the properties of the move and the layout of the level, then I've found a way to create the shortcut.
I don't remember seeing it in speedruns before my discovery, and at the same time I find it strange. I mean, when you know how that move works, it's not that big of a leap to use it in special ways like this. Someone correct me if it was actually a thing before the first Amy TAS :P
It's hard to tell for every glitch or trick if you're the first one to find it, but that doesn't remove the satisfaction of discovering it by yourself.
I did find some glitches in other games, like Sonic Triple Trouble or Donkey Kong on GameBoy (aka "DK 94"), but no practical use for most of them.
Edit: ah, more recently there was Zookman ZX4, I did get some minor glitches, but anyone who played the game did find many glitches by just playing casually without even trying :D (the biggest glitches are anoher story)
