On my first playthrough of Skyrim, the first questline that I did was the Dark Brotherhood's. I had really enjoyed the DB quests in Oblivion and as such wanted to get in with the assassin's right away. I played through the questline, earning the right to ride Nightmare, the greatest of all horses! Too bad it just up and vanished on me by the time I finished up the questline. Oh well, easy come, easy go I suppose. I proceed with the game, completing the Companions, then the Mage guild, then the Thieves Guild, and even the main storyline. All that was left was the civil war so I started that up. At one point I was just outside of Markarth when a dragon decided to drop in and say hello. It lands on a hill near one of the farms right outside the city and starts fighting with the guards. I start running down the road when I see a guard and a horse come running up over the hill that the Dragon was on and engage. I didn't think anything of it, figuring it was just some mounted soldier who had dismounted to join the fight and his horse was coming along with him. Now at this point in time I was a Stage 4 vampire, and this was long before Dawnguard came out...so people were ready to attack me on sight, but with a dragon about there were bigger things to worry about for the moment. Once the dragon was dead, however, the surviving guards turned on me...but not the horse. The horse was actually fighting the guards! Come to find out, it was the Nightmare! Returned from the depths of Oblivion, apparently, as I had literally played through the vast majority of the game with that horse being nowhere to be found.
More recently - and this is probably more of a humorous AI bug than an actual glitch - I was doing a quest for the Thieves Guild to unlock one of the special vendors in the Ragged Flagon's tavern area. The quest required me to delve into a cave full of bandits who had stolen something from the client and the client wanted me to steal it back. It was just a bunch of bandits, so I could have easily just slaughtered my way through the cave and snatch my prize. But I felt like being sneaky this time...I was working for the Thieves Guild at the time, after all. So I sneak through the cave and come to a chamber that the bandits had turned into a little bar with 3 bandits drinking around a table with a 4th standing behind the bar itself. I pickpocket them all, loot the shelves and whatnot, and proceed down the next tunnel. Before heading down it, however, I notice that there's a note pinned to the wall at its entrance, being held in place by an iron dagger. I go to read the note, but accidentally grab the dagger instead. Well an iron dagger is absolutely worthless to me, so I simply drop it, read the note, and move on. I'm snooping around in the next chamber of the cave when I notice one of the bandits from the bar coming down the tunnel. I quickly move to a dark corner of the room, but moved through a patch of light so the bandit half-spotted me. She pulled out her sword and starts searching, but after a few moments of me crouching silently in the shadows, she gives up and sheaths her sword while standing a few feet in front of me. My "stealth eye" is completely closed, so I'm completely undetected, yet the bandit just walks right up to me and says "You dropped this back there, I figured you would want it." and up pops the update "Iron Dagger Added". I just found it to be incredibly silly that this bandit - whose natural disposition towards me should be defaulted to hostile - decided to do me a kindness and return the object that I so carelessly dropped before walking back to the bar chamber to continue drinking with her bandit buddies.
Other than those two, does the Skyrim Giant's Space Program count as a "glitch"? Or is it intentionally programmed that every time a giant does its ground-slam attack with its hammer, it launches the target into orbit? I could never figure out if that was a glitch/bug or if it was intentionally made that way...but to this day every time I see it happen I'm brought to tears from laughter. Especially if the target is someone wearing Plot Armor of Invincibility, as they always end up coming back up to you as though they hadn't just gotten to take an express tour of the stratosphere.