I had a greyhound for a few years that was a good hiker dog. She could be off lead (but we did months of training to get a solid recall before she was off lead in strange places). With the thin, tight skin and sparse coat she would always get scrapes and cuts. They're limited as to season, they have trouble with heat and cold because of the low body fat content, but she didn't mind going out for a run in a coat and booties.
Other than that, I've hiked mainly with giant breeds, primarily livestock guardians (Pyrs and Kuvaszok). My concern with giants is that I'd be unable to pack them out if they got hurt.
I think a mid-size dog with a medium build and a medium coat would be best. The Border Collie meets those criteria. Mid-size because you could carry them if you had to, medium coat would allow hiking in all seasons, and medium build would avoid extremes of type (think whippet vs. st. bernard). Lighter coat colors tend to have an easier time with the heat because the coat doesn't suck up the heat from the sun the way a black coat does.
As for attitude, in general both herding and gun dogs are trained fairly easily, and tend not to have strong guarding instincts. I find that herders can be a bit more reactive and aggressive than gun dogs, but the nature of the job they've been bred for requires a bold personality.
This isn't to say that there are breeds that can't hike - I've seen lots of dogs in the woods - just that some might tend to be a little better. And don't forget, any dog will need to be gradually conditioned physically and mentally to become a good hiker-dog, and not all dogs can or want to hike.
I love Border Collies, but I could never live with one. I don't think I'm smart enough to stay one step ahead!
