Obviously, the horse's mind is paramount. Make sure the horse likes to move out. Not stupid crazy move out or you will find yourself fighting for completions (and maybe to stay on!), but willingness to hit the trail and go to work. I have seen some horses that seem like they'd be awesome at endurance, but they were a psychotic and ended up getting pulled a lot. Check out Arab crosses, too (like an Arab/Appy or Arab/QH or Arab/Mustang). Sometimes the cross will bring something really amazing to the gene pool (I have an Arab/Welsh cross and she's wonderful, but the friend I ride with has a very amazing purebred Arab that is rock solid in the brain).
A horse that has decent athletic ability and an amazing mind is WAY better than the horse that has incredible athletic ability and is totally cuckoo-pants. It is easier to get a horse conditioned if s/he isn't wacko, and, IMHO, it's easier to get a sane horse into the top ten than the one that is fast but nuttier than squirrel poo.