Germany is in the Schengen area, a collective of 26 European countries that have eliminated passport and immigration controls at their joint borders. So any citizen of these 26 countries can travel freely through this area.
Nationals of EU and EFTA (Iceland, Norway, Switzerland, and Liechtenstein) countries only need a valid passport or national identity card for entry - they will not need a visa for a stay of any length. This includes the UK.
Nationals of non-EU/EFTA countries will generally need a passport in order to enter a Schengen country, and most will need to get a Schengen visa.
Citizens of the United States of America can enter Schengen countries without getting a visa as long as they hold a valid US passport and do not stay longer than 90 days within a 6 month period.
Wherever you're travelling, you should always have your passport or ID card with you.