Fafnir was the brother of Otr and Regin. When Otr was killed by Loki, Fafnir covered his brother's body in gold. Fafnir got into a disagreement with Regin, and changed himself into a dragon. He and Regin were killed by Sigurd.
Another version of Fafnir was a giant who, along with his brother Fasolt, built Valhalla. In exchange, they asked for the goddess Freya in marriage. Odin offered them gold instead, and Fasolt accepted it. Fafnir kiled his brother to get all of the gold for himself, and in order to better guard his treasure, transformed himself into a dragon. He was killed by Sigurd on Glistenheath. By eating Fafnir's heart Sigurd gained the ability to talk to and understand birds.
In art, Fafnir appears as a dragon, or as a man wearing the Helmet of Dread (Aegis) on his head.