There are two basic types of beer: top-fermenting ales and bottom-fermenting lagers, with the sub-types being offshoots of those two bases. Beer guru Michael Jackson likens ales and lagers as the red and white wines of the beer world.

Ales Ales trace their history back to the early days of man, when the brewers weren't entirely sure how this beverage came to be--they just knew the necessary ingredients. Ales have been made for nearly 8000 years. The name comes from the German word 'alt' meaning old or aged. They are fermented at warmer temperatures and yield distinctive, fruity, robust tastes and are best consumed "cool" rather than "cold." Common ales: Pale ale, amber ale, porters, stouts, Belgian beers, wheat beers, and other specialties.

Lagers Compared to ales, lagers are tykes in the beer world, having only been brewed since the 15th century. As a bottom fermenting beer, lagers are fermented at cooler temperatures, helping the yeast to sink. "Lager" comes from the German "lagerung" referring to the cold storage necessary for the beer. Lagers are typically less fruity than ales, but are cleaner and rounder. Common lagers: Pilsners, bocks/doppelbocks, Maerzens/Oktoberfests, Dortmunders and other specialties.

Other styles:

Spontaneous Fermentation Beers under this category are naturally fermented by airborne "wild yeasts" and not the highly controlled conditions of cultivated yeast. Lindemans Lambics and Melbourn Bros. line of apricot, strawberry and cherry beers are made through spontaneous fermentation.

Bottle-Conditioned These specifically Belgian ales are fermented multiple times with extra doses of yeast added at bottling. They are complex, evolving and grow better with age.

Trappist ales fall into this category. Trappist ales are brewed by monks of the Trappist order; only six exist world-wide that brew Authentic Trappist Products.

Information gathered from:
http://www.merchantduvin.com
http://www.realbeer.com
http://www.beerhunter.com/styles/lager.html