The other main predator that also hunts in this fashion? Wolves/dogs. There's a theory that it was this overlap in hunting styles that made us natural "partners" and led to the close relationship we have today.
Wolves and dogs can't do this over nearly the same distance humans can — they shed body heat through panting and can only keep up a run for 3-6 miles[0]. Humans can run marathons.
Edit: I should say, wolves/dogs can run for long distances too, at a slower gait. But they can only out-pace human marathon-distance runners for a few miles before overheating.
Edit 2: Found a source[1]: "Dogs can gallop for only about 10 to 15 minutes before reverting to a trot, and so their distance-running speed tops out at about 3.8 meters per second." As commenters below have pointed out, yes, if it's cold enough, this doesn't matter ;-).
Well, I don't know much about wolves, but I know dogs sometimes naturally track interesting prey over long distances by scent. They don't have to travel fast, they just have to travel on average faster than their pursued prey.
I don't know. In Herzog's "Happy People: A Year in the Taiga," you see a dog keeping up with a snowmobile at a constant pace for several hours. (Edit: the dog ran 150 kilometers nonstop at a snowmobile's pace)
Sounds consistent with Walking with Cavemen in which they related the hypothesis that the human nose is so protruding so that it can be breathed through for temperature control, rather than by panting which loses water.
