Skodi Skeggvason cut off Ullveig Helgasdottir's hair after defeating her in combat. Shamed by this, Ullveig vowed not to grow her hair back until Skodi is dead.
Ullveig later erected a nithing pole (with one of the Skeggvarshold draft horses chopped-off heads on top!) declaring that she wouldn't marry or regrow her hair until Skodi was dead.
Ullveig later ambushed Skodi, got her ass kicked again, and was taken prisoner by the Skeggvasons; after some negotiations and Skodi magically reattaching her hair and rings, she "escaped" and has declared the feud over.
The Skeggvarsons have thrice thwarted Droskar, the evil god of the gray dvergr (or the duergar, as they are called in Common). They slew his forge-spurned and freed the innocent souls it had forged into its chain; they revealed and helped destroy the Droskar Cult among the dvergr Rune Guild in Orkafjall; and they protected Svirkr Firetongue, former leader of the Droskar Cult, as he atoned for his heresy by slowly killing himself in the Teeth of Torag.
This is not exactly a feud, but presumably Droskar is not going to take this lying down. On the other hand, it's not clear what if anything he can do in the surface world – his worshippers largely live in Svartalfheim.