|MadSci Network: Anatomy|
Identifying animals from skulls is an important part of zoology -- since most of the animals that have ever lived are no longer around, often we have nothing but a skull to work with. Since you described the incisors and molars in your skull, I assume it's a mammal skull, because reptiles don't have differentiated teeth like that.
In order to describe the exact animal, a zoologist usually needs to know the number and shape of each kind of tooth, as well as the size of the skull, and often several other characteristics. From the information you gave me, I can't pin it down specifically, but I can narrow it down a lot.
You're writing from the USA, so I'll assume it's a native American mammal. There are eight major Orders of mammals in the United States (aside from humans): Lagomorpha (rabbits and hares), Rodentia (rodents, including squirrels, mice, rats, beavers, groundhogs, and gophers), Xenarthra (armadillos), Didelphimorphia (opossums), Artiodactyla (deer, moose, elk, etc.), Carnivora (cats, dogs, wolves, bears, raccoons), Insectivora (moles and shrews), and Chiroptera (bats).
You say the skull is two inches wide and five inches long, which is too large to be a bat, mole, or shrew, so those two Orders are out. Similarly, it's too small to be in the deer family (in addition to which, the deer family usually don't have upper incisors, and you specifically mention the incisors). Armadillos don't have incisors either, so it's not one of those. That leaves four possible Orders.
You say it looks like a beaver skull, but smaller and "more carnivorous." I'd need more information to tell you exactly what it is (and know what you mean by "narrow" molars), but I can tell you how to figure it out:
If your skull has prominent canine teeth (they'd be the ones immediately posterior to the incisors), it's probably a carnivore or an opossum. Opossums have five upper incisors on either side of the jaw (ten in all); carnivores have only three (six total). If it's a carnivore, it's probably a small dog, or maybe a fox -- at that point, you'd have to look at specific features of the skull to tell what it is.
If your skull has no canine teeth (which I would guess is the case, since you didn't mention any), it's either a rodent or a lagomorph. The difference is that lagomorphs have two upper incisors (four total), where rodents only have one. The second pair may be hard to see: they're very small and sort of behind the larger incisors. If your skull has only one set of upper incisors, it's probably either a beaver or a groundhog. There aren't many other rodents that have five-inch skulls.
The process of identifying an animal by the features of its skull (or any other features) is called "keying," and requires a key. Keys usually follow a binary (two-part) pattern like the following:
1a. Canine teeth are present. Go to 2.
1b. Canine teeth are absent. Go to 3.
2a. Skull has one set of upper incisors: Order Rodentia.
2b. Skull has two sets of upper incisors: Order Lagomorpha.
3a. Skull has five upper incisors: Order Didelphimorphia.
3b. Skull has three or fewer upper incisors. Go to 4.
... and so forth. There is an excellent key for skulls available from Texas Tech University Press called "Illustrated Key to Skulls of Genera of North American Land Mammals," by J. Knox Jones, Jr. and Richard W. Manning. It has a key, as well as pictures of many of the skulls and a comprehensive glossary. If you're going to be doing some skull work, it would be worth your time to locate a copy of this book.
Try the links in the MadSci Library for more information on Anatomy.