There are basically three types of beer, ales, lagers and speciality beers. Ales are generally more known for their higher alcohol percentage and fuller more complex flavors. Lagers are famous for their drier taste and lighter color. Speciality beers are often a combination or an ale and a lager or they use special ingredients like spices or fruit.
Some famous styles of ales:
Belguim Strong Dark Ale
Some famous styles of lagers:
Some famous styles of speciality beers: