If you are a citizen of one of the 22 European Union countries, you do not have to have or present a passport when traveling between Schengen member countries. All European Union countries are Shenegen member countries except for the United Kingdom, Ireland, Romania, Cyprus and Bulgaria. If you travel between Schengen member countries, you simply need to present an ID card to prove your identity and citizenship. Most likely you will not need to show any identification at all, as there are no longer internal boarder controls in most European Union countries. Whenever you leave the European Union, you must provide a valid passport.
If you are a citizen of the United Kingdom, Ireland, Romania, Cyprus or Bulgaria, you need to present a valid passport to enter all other European Union countries. Whenever leaving the European Union, you must also provide a valid passport.
Though not in the European Union, these four countries are members of the Schengen member countries. Citizens of these countries may travel within the European Union Schengen member countries without a passport, though if exiting a Schengen member country or the European Union, must provide a valid passport for exit and re-entry.
Non-European Union Citizens must provide a valid passport when entering and exiting the European Union. While in Europe, you will most likely never be asked for your passport while traveling internally throughout Europe because there are no longer internal boarder checks. It is always wise to have your passport available, however, because internal boarder checks could be instituted during times of heightened national security. Depending on your nationality, you will also need a visa to enter most European countries. For United States citizens, most European countries allow entry for up to 90 days without a visa.