There are basically two different kinds of grinders: blade or burr.
Most inexpensive grinders use a metal blade to chop up the beans. The blade cuts up the beans, and you control the fineness by how long you let the grinder run. Unfortunately, the resulting coffee grounds can be uneven in size, leading to inconsistent brew quality. Another downfall, is that if you are grinding finely, and therefore leaving the beans in the grinder for a longer period of time, there can be significant heat created by the blades. This can give your final coffee a burned taste. These are fine grinders for basic use, but that's about it.
Burr grinders crush the beans between a moving grinding wheel and a non-moving surface. The positioning on the burr is what regulates the ground size, which allows for a more consistent grind. In the burr category, there are two different types.
Wheel Burr - The less expensive of the two burr grinders. The wheel spins very fast, and these grinders can be noisy. The higher speed rotation make these grinders more messy as well.
Conical Burr - The best grinders you can get are conical burr grinders. The burr spins slower than the wheel model, which makes them quieter and less messy. You can use a conical burr grinder for oily or flavoured coffees and it's not likely to clog, like the other kinds of grinders. These are the best type, but you will pay the price for them.