This was at the point when I was messing around with mods and the console, so I'm not sure what caused the bug.
I was wandering, when I was set upon by not one, but TWO dragons. So I got into the battle, and out of nowhere I absorbed the soul of one of them... while it was still alive. So I was fighting one dragon that was just a skeleton.
Then, once that one was dead, I realized the other dragon was invisible. It stayed invisible even after it died.
That's not the best bug I've seen though. This one happened to a friend who was playing Skyrim at my house.
She had gotten married to Farkas, but he'd gotten killed during a dungeon run. Well, everything was normal, she'd looted his body (and tried unsuccessfully to revive him), then sold his wedding ring and gotten herself a new companion. She and her new friend were wandering Skyrim when suddenly she saw something coming down a mountain at her. It was Farkas, back from the dead and stuck halfway in the ground.
He seemed fine, and even agreed to follow her again. After fast traveling, he was out of the ground and a full character again. Before being killed shortly after.
We laughed about that one for quite a while afterwards.