It depends. Long or short? Hot or cold weather?
I have a Saluki, two Borzoi, a Great Pyr, a Schipperke, and a Shiloh Shepherd.
The Pyr usually stays at home because he's so big, unless it's a short hike. Pyrs also have thick coats that make them overheat easily, and it's dangerous to shave them because of sunburn and skin cancer.
The Schipperke stays home because he's too little to swim across rivers, and he 's usually muddy, so I don't want to carry him.
The Saluki and the Borzois do GREAT, because, well, they're hounds, obviously. I've done overnight hikes and covered 40 miles in a single day (it was an endurance event), and the dogs LOVED it.
However, I wouldn't feel safe (hounds aren't aggressive towards bad people) without my Schutzhund-trained Shiloh Shepherd, who also has good endurance (though not as good as the hounds, and is a lot more intimidating to a suprised psycho.
Just make sure to keep your dogs on a leash!
I'd advise a hound breed, like a Bluetick, Saluki, Borzoi, Rhodesian Ridgeback, or something along those lines. Hounds have great endurance and stamina, as well as speed.