This article is from the Hiking/Backpacking With Canines, by Terri Watson with numerous contributions by others.
From the human perspective, basically most people that can go hiking
without a dog can go hiking with one. The additional constraints are
that you must be (1) physically able to restrain your dog (or dogs) in
the presence of distractions, such as a running deer or squirrel, and
(2) responsible enough to prevent the dog from being a nuisance to
other people or animals. This includes picking up after your pet.
From the canine perspective, if the dog is healthy, fit and
well-behaved around other people (both adults and children) and
animals, she can usually accompany the owner(s) on their outings. Of
course, for both humans and dogs, a visit to the doctor to evaluate
general health is a good idea before starting or increasing physical
demands. Particularly if you choose to have your canine carry a pack,
you should be confident they are in good health and structurally
sound. Consider having your dog's hips X-rayed in order to check for
hip displasia before asking him to carry a full pack over long
distances. Dogs, like people, need to gradually build up strength and
endurance. See the section on packing with your dog for more
information on conditioning.