Citizens of the EU will not need a visa for travelling within its boundaries. However, a passport or identity card is required. More information on the free movement of people within the EU can be found here. Make sure that any children travelling with you either have their own passport or ID card or are registered on your passport. By June 26, 2012 all children who wish to travel will have to have their own passport.
Those who are not citizens of the EU will need a valid passport. Certain nationals do not need a visa to visit the EU for three months or less. More information about visa requirements for non-EU citizens, including a list of countries whose nationals require a visa for travelling in the EU, can be found here.