Given what I see on the trail and read in the papers I'm in the minority, but...
Dogs should always, always be on leash. It's best for the wildlife and others on the trail but, more importantly I think, it's best for the dog. A couple times each year, my local paper runs stories of dogs caught in traps. They're pretty sad stories. And of course there are other 'threats' to domestic dogs in the wilderness.
I backpacked with a wonderful Samoyed for six years...he was never off lead which was hooked to his pack harness. That came in quite handy when he slipped off the narrow trail and into the fast running Eagle River just outside Anchorage.