A couple of weeks ago, a friend of mine gave me some samples of Longwool Leicester (I'm never sure of the order of the words for this breed) and some chiengora (dog hair + wool) to try out. The LL was not at all enjoyable to spin. It was a woolen preparation which, with such a long staple, made it extremely hard to spin. If it had been in a combed top preparation, it would have been much, much easier to spin but you would still have the fact that it's a coarse wool that can't be used for anything that might be in touch with your skin. It would be find for a rug or placemats if they were woven or even for a tapestry but it would not have been very nice to knit. I'll bet it would take dye wonderfully, though.
But the chiengora (chien is French for dog and this is the name that many people use for yarn made from dog hair/fur) was a dream. It's 25% Samoyed and 75% wool and it's the nicest, non-doggiest feeling chiengora I've ever spun. Not sure what the wool is but the mixture is spinning into a nice, soft yarn.
Have a look here for more information about chiengora. You can also have your dog hair processed into yarn from these folks. I have no experience with them and don't endorse them. I'm simply providing the link for informational purposes. Here's another link with some info. And here.