German beer is dominated by pale pilsner style lagers brewed to the ancient standard of the Rheinheitsgebot and are held in high regard the world over generally.   The excellent German Beer Institute - see link above - lists sixty three(!) different styles of German beer, but I will mention in this article just the most popular ones:

Pilsner - Classic hoppy pale lager style beer.   Also called Pils.

Weissbier - Unfiltered wheat beer.

Kristallweizen - Filtered, clear wheat beer.

Bock - Strong malty lager.

Altbier  - Top fermented and copper to dark brown in colour.

Helles - Pale lager.

Kolsch - top fermented pale lager style beer.

Dunkel - dark lagers.

Dortmunder - Hoppy pale lager from the industrial Dortmund area.

Kellerbier - unfiltered, hoppy lager.

Rauchbier - Smoked beer.

Popular examples are:

Pilsners

Bitburger Pils, Jerver Pilsner & Veltins Pils.

Dortmunder

Dortmunder Unions Brauerei & Dortmunder Actien-Brauerei.

Wheat Beer

Erdinger Weissebier, Maisels Weisse & Scheider Weisse.

Kolsch

Fruh, Gaffel & Kuppers.

Altbier

Bolten Alt & Schlosser Alt.

Rauchbier

Aecht Schlenkerla Rauchbier Marzen.