Looking at the selection of skulls we examined, the first thought, from an anthropic standpoint, would be that the skulls of other the other animals seem like elaborations and expansions of the human skull. Our jaws, compared to the distended shapes of those of, say, porpoises or dugongs, appear small, compact, and relatively simple, and our teeth seem similarly diminutive and similarly uncomplicated.
The explanation for human jaw proportions (from the Discovery Channel; make what you will of that) is that the invention of fire and therefore of cooking made the chewing of food easier. The necessity of biting through and masticating raw meat gone, jaws could shrink without unpleasant evolutionary consequences. The results of that not happening, I think, are visible in the skulls of the other primates we looked at. Both the gibbon and the gorilla had particularly large canine teeth, suggesting (assuming that, like humans, gorillas and gibbons are omnivorous) that the chewing of meat was the real issue at hand, the problem of how to deal with fibrous grass and foliage presumably requiring more radical adaptations.
Aside from size, I surmise that humans and the above-mentioned other primates eat in much the same way. The incisors and canine teeth tear or scissor off pieces of food, which are passed backwards to the molars to be ground down prior to swallowing. While not identical, teeth of these kinds in humans, gibbons, and gorillas are extremely similar; molars are all broad and roughly cylindrical, canines terminate in a point, and incisors narrow to an edge. Another similarity: the near-invisibility of the premaxilla as a distinct bone separate from the rest of the jaw. By contrast, the premaxilla, in the remainder of the animals, is generally quite distinct.
In grazing animals, such as the horse, and rodents, such as the capybara and the beaver, the premaxilla protrudes, like the bow of a ship, from the remainder of the jaw, which contains the molars. The reason for this, I think, is because there is a greater distinction between the roles the teeth play. In humans (and presumably other primates), teeth can perform each other's tasks somewhat interchangeably: incisors aren't wholly unsuited to chewing; molars just do a better job. Molars, depending on the food, can cleave off pieces as well. Contrast this with how a grazing animal would eat: the incisors clip off pieces of plant matter, which is passed backwards for prolonged chewing. In that case, a long row of molars, set far back from the mouth's front (possibly allowing for biting and chewing with the same movement), is more efficient at processing large amounts of grass than humans' compact jaw layout could ever be. A similar sharp distinction in function seems apparent in rodents, whose large incisors appear to play the predominant role in eating, shaving or tearing off small, manageable chunks of food. The molars are greatly reduced, possibly to (as in hamsters) allow the cheeks to serve as storage space, possibly because the individual pieces of food being dealt with aren't particularly substantial. Human mouths here occupy a “jack of all trades” role, with teeth and jaw portions not only shrunken but less differentiated.