One Protoceratops, a herbivorous (plant-eating) dinosaur, perished in the struggle with a carnivorous theropod, Velociraptor. After their death 80 million years ago, both skeletons were fossilized, then finally unearthed in 1971 in fully articulated forms without having been smashed.
However, not only is it real, it's one of the most famous fossils in the world. It was found in Mongolia in 1971, and was exhibited in 2000 at the American Museum of Natural History. An episode of Discovery Channel's Dinosaur Planet included a computer-graphic reconstruction of the struggle between the protoceratops and the velociraptor. The fighting dinosaur website seems to be circulating around right now because someone linked to it on digg.com.
The big mystery is how the two dinosaurs managed to get buried alive while fighting. Dinosaur Planet's theory is that "the animals were most likely fighting on a rain-soaked sand dune which collapsed preserving them mid-battle." Or they could have gotten stuck in a sudden sandstorm. A few other theories are outlined in a post on cryptozoology.com.