I plan on getting you a better answer for this, I have a good friend who is an animator at PIXAR (Toy Story, Monsters, Inc., The Incredibles). But I believe I'm correct in saying that the "styles" are generally referred to by either the individual or studio that pioneered them.
One I am positive about is called "UPA Style." This refers to the United Productions of America animation studio that pioneered a look that became popular in the late 40's and 50's... Gerald McBoing Boing, Mr. Magoo and others used this thick and thin outline style, sometimes colored by simple blocks of color behind the lines. Disney picked up on this style for their famous "Toot, Whistle, Plunk and Boom," which you might remember.
Wikipedia has an excellent entry for UPA:
http://en.wikipedia.org/wiki/United_Productions_of_Ameri ca
I'll see if I can learn if there are similar names for Disney, Hanna Barbera, Warner Brothers/Chuck Jones and others.