I am assuming you are a non-EU citizen who has a residence permit for Germany (Niederlassungserlaubnis). You want to know how many countries this allows you to visit without having to get a visa.
The answer is all countries which are part of the Schengen Area. That is currently 26 countries:
Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden and Switzerland.
Bulgaria and Romania are due to join Schengen in 2013. Norway and Switzerland are not part of the EU, but are in the Schengen Area.
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