How Long Do Patents Remain Active?

In general, the "lifespan" of a patent will be 20 years from the priority date.

This, however, is a very general rule. Individual rules on the lifespan of patents can  be found in the following WIPO document:

http://www.wipo.int/export/sites/www/standards/en/pdf/archives/03-09-02arc2008.pdf#search=%27Germany+utility+model+patent+expiry+date+three+years%27