As an european resident you may travel to any european country without a visa. Though all travellers do need a valid identification document, like an ID or passport.
Some european countries settled on the abolishion of systematic internal border controls in the Schengen Agreement. They further arranged that for entry or exit every person at the external borders has to show a valid identification document.
Hence you have to ensure to always carry a valid identification document with you.
Members of the Schengen Agreement: Belgium, Denmark, Germany, Finland, France, Greece, Iceland, Italy, Luxembourg, Netherlands, Norway, Austria, Portugal, Sweden, Switzerland and Spain. Please consider that no all these countries listed above are members of the EU.
For further information visit the homepage of the Federal Foreign Office.
To simplify and speed up the customs clearance seperate checkpoints for travellers from EU/ Schengen countries and travellers from Non-EU/ Non-Schengen countries are installed at airports. They are marked as "EU" respectively "No-EU-National".
As a Non-EU resident you need a valid identification document and a visa. Further information considering regulations about visa and exceptions are available at the Federal Foreign Office.
Please inform yourself on the following site of Customs online, what kinds of souvenirs and in which amount are allowed to be imported to Germany.
Since June, 15th 2007 there is an obligation to declare cash money in all countries of the european union of 10,000 or more during entry and exit of the EU external borders.
For further information please visit the homepage of German Customs.
If exiting the EU, declarations for cash money have to be done prior to check-in at the customs office.