Wulf

Kill them all and let Odin sort them out.

Wulf is a Viking warrior whose recklessness brought him into contact with Morginne, a powerful Dark-Huntress. She tricked him into trading souls with her.

He is the only Dark-Hunter who was never granted an Act of Vengeance. And since he was wrongfully brought over by another Dark-Hunter, his powers are very different from the rest of his brethren. The most curious power of all, is that of amnesia. No human or animal is capable of remembering him five minutes after they leave his presence. The only exceptions to that are those who bear the blood of his original Squire.

Since the only out-clause for a Dark-Hunter is the love of a human, and no human is capable of remembering him (and by the Code of a Dark-Hunter, no Hunter can be physically or romantically involved with his Squire), Wulf, alone, is doomed to an eternity of Hunting.