This happened to me just last week. There's this PS1 game called Omega Boost, and it's a Starfox clone/giant robot game from Polyphony Digital, the studio better known for the Gran Turismo games. It's also one of the prettiest games on the system, but that's beside the point. The point is, I was playing it last week when I decided to hit the L3 (or was it R3? I can't remember, one of the buttons on the analog sticks) button and push the stick in a random direction. It initiated an instant 180, allowing me to turn around very quickly and making some very annoying boss fights much easier.
I've had the game for at least 10 years now, and I never knew you could do that. I even have a complete copy and have read the manual several times. Either it doesn't mention that feature, or I just never noticed it before. Either way, total fail on my part.