Some nice (and from what I know, mostly accurate) observations of the Covenant.
Socrates (firstname.lastname@example.org) writes:
I theorize that, aside from the Hunters, every member species of the Covenant is a carnivore. The basis of my theory is made on the jaw and tooth structure of the individual species. The sharp, inwardly pointing teeth of the Grunts, Jackals, Brutes, and Elites indicate a diet of meat.
These kinds of teeth are used for tearing and holding meat in the jaws. In the Elite, the jaw structure suggests that the Elites or their ancestors favored eating small animals and, like snakes, not waiting to kill their prey before they ingested it. Jackals or their ancestors probably had similar diets. The Brute's jaw structure and tooth arrangements indicate that they (or their ancestors) prefer larger prey, taking chunks of meat out of prey they killed. The same probably goes for the Grunts, though I suspect that the Brute/Brute ancestor likely hunted alone or in small groups, while Grunts/Grunt ancestors likely hunted in larger packs.
[Or could be scavengers considering relative size - editor]
(Interesting, if gruesome, side note about the Grunts--the contents of their "Food Nipples" are likely puree'd protein. I'll leave it to the reader to imagine the source of said protein.)
I haven't been able to get a good look at a Prophet's tooth structure but, from what I have seen, it is composed of densely-packed, sharp-tipped teeth that would also indicate a carnivorous diet.
I have also been unable to get a good look at the mouth structure of the Drones, but it seems to me that their ant-like preference for swarming and their size both indicate a carnivorous diet. The size or the swarming characteristics, taken alone, could indicate an herbivorous diet; however, as the Drones exhibit both, I believe them to be carnivorous in their diet. (Entomologists, please feel free to correct me if I am wrong!)
As for the Hunters... well, anyone's guess as to their diet is as good as my own.