One of the biggest debates: was T. rex hunting, or snacking on the already-dead? Although so many theropod teeth are found throughout excavations of prey animals (like Triceratops or duckbills), that's not enough to say whether T. rex was eating something it killed...or something it found.
This is a fun argument, because it allows us to evaluate some of T. rex's most impressive parts. A brain packed with the capacity to smell well, see with precision and in three dimensions; a body with legs that could outrun prey, with deadly teeth and claws for killing, and an efficient breathing / circulatory system meant to fuel an athlete. T. rex certainly had the equipment.
Today's scavengers act as excellent models - and these models show that no large-bodied creatures rely solely on scavenging! Hyenas, for example, kill more than they plunder. Only vultures rely mostly on scavenging (but they'll kill, too, when they're hungry enough), and they are built differently - with wings to cover lots of territory, no binocular vision, and a not-so-great ability to smell.
The fossil record also proves this point: "the one that got away." In The Denver Museum of Nature and Science, a duckbill dinosaur is on display with a healed bite mark at the base of its tail. Triceratops specimens also have been found with similar healed injuries - injuries that could not have been made in the Cretaceous by anything besides T. rex's mouth. Remember: the fact that these bites were healed means the animals were alive when they were attacked!
Even worse: a few cases of T. rex cannibalism have been discovered. Not only does it seem that T. rex was a killer, apparently no one was safe. Scientists have found at least two instances where T. rex vertebrae were sheared in half, and the parts where T-bone and tenderloin steaks would have been were missing. No one else had the jaws to do it.
Sue's crime scene also preserved some interesting information. Black Hills Institute workers found fragments of three other T. rexes, one of which was a lower leg that was sheared in half - the fine scratch marks matched the serrations of a T. rex tooth. In related news, Sue's skull shows the unmistakable marks of another T. rex, who literally ripped off part of the left side of her face. Maybe her skeleton was preserved (and not eaten), because the perpetrators had filled up on those other T. rexes with her.
'You know,' he added very gravely, 'it's one of the most serious things that can possibly happen to one in a battle - to get one's head cut off.' - Lewis Carroll, Through the Looking Glass
Keep in mind, though, we don't have to limit our thinking to predator or scavenger. Most creatures will eat what they can get; this is known as opportunistic feeding. Just like a lion will snack on a free, already-dead, smelly meal if it finds one - or a vulture will kill if it's hungry enough - we suppose T. rex wasn't choosy. Predator or scavenger? YES!