How is beer classified into different types? How is beer classified into different types?

Can the types of beer be arranged in a hierarchy with "ales" and "lagers" at the top? Are there beers that do not fall under either category or some that fall under both? 

What are the divisions under these categories? 

What are the defining characteristics distinguishing one type of beer from another?
http://beeradvocate.com/beer/101/ has a vast amount of information on beer styles.

To answer your specific question, an ale is top-fermenting whereas a lager is bottom-fermenting. Lagers are generally fermented at lower temperatures than ales.

I believe that lambics would constitute a third category, since they are traditionally fermented by wild yeasts, but opinion may vary on this, I don't know.

There are dozens of styles of ales and lagers and a few different lambics, but the method of fermentation is the main distinguishing characteristic between the three types.