The Federal German Ministry of Justice and for Consumer Protection (Bundesministerium der Justiz und für Verbraucherschutz) provides translations of a number of German laws. These translations can be found here.
Especially of interest might be:
a) The BGB - German Civil Code:
The BGB (Bürgerliches Gesetzbuch) is the Basic German Civil Law Statute and apart from the Grundgesetz (German constitution) probably the most important statute in Germany. The BGB regulates most areas of German private law: law of contracts in general, tort law and compensations, property law, family law (esp. marriage and divorce), law of succession (esp. wills).
BGB in German: Click here
BGB in English: Click here
For more information on the BGB see the english Wikipedia.
b) Strafgesetzbuch - The German Penal Code
The Strafgesetzbuch includes criminal offenses and punishments in Germany, from murder to burglary, treason to "Using symbols of unconstitutional organisations", fleeing the scene of an accident (Yes, in Germany, that is a criminal offense) to DUIs.
Strafgesetzbuch in German: Click here
Strafgesetzbuch in English: Click here
c) Aufenthaltsgesetz - Act on the Residence, Economic Activity and Integration of Foreigners In Germany
Aufenthaltsgesetz in German: Click here
Aufenthaltsgesetz in English: Click here
Regulates under which circumstances foreigners may live and work in Germany.
Please note that these are not official translations. Also the Ministry states:
"Translations of these materials into languages other than German are intended solely as a convenience to the non-German-reading public. Any discrepancies or differences that may arise in translations of the official German versions of these materials are not binding and have no legal effect for compliance or enforcement purposes."
Still, I think they are very useful to get an understanding of German laws.