My Favorite Glitch
I've had several glitches, but my favorite was when I tried to get married.
Lydia had been my follower, but had died in some random dungeon. When I tried to get married her dead body showed up at the wedding and the wedding would fail. I tried several times and her dead body would always spawn at the door of the temple of Mara, upsetting everyone at the wedding. I had to go back and apologize to Vorstag to get him to marry me. After we were married and living in Whiterun Lydia's dead body was on the floor in the spare loft room for several weeks before disappearing.