I don't have a video of it or anything, but the best glitch I ever found, to the best of my memory was back when I was playing Elder Scrolls: Oblivion. I was playing as an Argonian and went over to where the portal to the Shivering Isles were. That big booming voice came, rambling on and I was like, "Okay fine, I won't go inside. Jeez..." And walked away, to continue on doing what my Argonian loves to do. Stealing things.
Later, I was in a city all the way across the map from where that island was and I picked a lock to get into someone's house. No sooner did I get inside did suddenly something trigger the voice from the island to go off and start yelling at me. I freaked out, thinking it was a guard and ran out of the house... right into a guard's waiting hands....
... And thus is the story of why my Argonian, Dreekius, is now considered throughout the land of Cyrodil to be Schizophrenic....