I have plenty of great stories about me experiencing moments of skillfull glory, but the funniest and most memorable tales are usually about accidents.
My personal favorite is when I was taunting with the Sandman in an attempt to kill a zoomed-in sniper in front of me in order to unlock the respective acheivement. I wound up, but, as usual, the sniper strafed to the side just far enough to dodge the attack. Just as I had lost hope for this attempt, a teammate ran past, followed shortly thereafter by another teammate who happened to be right in front of me as I swung. Low and behold (and much to his surprise), the "teammate" in front of me spontaneously turned into an enemy spy as I hit him, and promptly went flying halfway across the map. He probably remembers it as the worst moment of his spy career, but it's certainly the funniest spy moment I've ever seen.
Oh, yeah, and my best moment of badassery with any class was when I was playing as a sniper and got charged, at close range by a scout, soldier, and demoman, all at the same time. It was an open area on a surf map, I was standing on top of a wall, the soldier was on the wall to my left, the demoman to my right, and the scout was below us, firing up at me. I got a headshot on the scout, killing him instantly, dodged the soldier's rockets while getting two succesive heatshots on him (the latter of which was lethal), and got several more shots on the demoman, finally killing him with a heatshot only to be gibbed moments later by a posthumously detonated grenade. I felt awesome about this at the time, and only more so as time went, on, although I concede this particular instance involved some luck, and has not often been replicated by me.