This is kind of relevant: In Pokemon White, I was training in the Desert Resort and happened to wander north towards the Relic Castle. Once inside, I was challenged by a certain psychic, whose only pokemon was a level 20 Sigilyph. I think all of my pokemon were about level 15 or so at that time, and that Sigilyph was a beast with his Psybeam. It wiped out five of my team members, and much to my horror, all I had left was a level 13 Throh that I only had in my party because I was going to trade it later for a Tepig. The Sigilyph was considerably weakened at this point, but I figured it wouldn't matter since it would no doubt Psybeam or Air Cutter the Throh and one-shot him, as both would be super effective. Sigilyph used Psybeam, predictably, and just when I thought it was all over, Throh survived. He was left with only a few hitpoints, but he somehow survived Sigilyph's devastating attack. I immediately retaliated and defeated Sigilyph.
You know the best part of that story? The trainer's name was Psychic Perry, and Perry is my name. Upon beating him I turned to my friend Michael and said,
"I have defeated myself!"
"You have deafeated your greatest enemy," he replied.
Man, that's like something out of the freakin' Twilight Zone.