ring Draupnir (which can be used to store evil spirits), they have plans of their own, separate from those of Odin and the other gods. Urd, in particular, is implied to be manipulating events on her own. In the anime, they have been sent to earth by Odin to kill Loki. Most of their attempts fall into the "Monster of the Week" pattern familiar to Super Sentai shows and magical girl/magical boy anime.
In the anime, there are many strong hints that Loki had an affair with Skuld in Asgard—an entire episode is even dedicated to this question which could be the Norns' fuel for 'hating' and helping him. It is not known for sure though. In the manga, Skuld certainly has a crush on Loki, but there are no hints of anything more serious.