The Strange Amulet from that murder investigation quest in Windhelm. I refused to sell it to the house of curiosity shop guy because I needed it for evidence. Now it's stuck in my inventory as a quest item and he won't offer to buy it off me anymore.
I had this happen on my first character too. And all of the Bard's college junk. And all of the Briar Hearts. And all of the Runed Lexicons and junk from that daedric quest. On my most recent character I so far only have the Elder Scroll stuck in my inventory, but since I have no intention of joining the Mage's Guild it's staying there.