Drewhound, it all depends on whether the countries concerned signed the Schengen Convention:
"Which EU Member States are now signed up to the Schengen Convention?
As of March 2001, 13 EU Member States are signed up to the Schengen Agreement. They are Belgium, Denmark, Germany, Greece, Spain, France, Italy, Luxembourg, Netherlands, Austria, Portugal, Finland and Sweden.
Ireland and the United Kingdom never signed up to the Schengen Convention and have thus not ended border controls with other EU Member States, although they will participate, in the future, in those aspects of Schengen that entail cooperation between police forces and the judiciary. For this reason, EU citizens, as well as third-country nationals, still have to show their passports when travelling between the UK or Ireland and the rest of the EU (although not between Ireland and the UK, which together with the Channel Islands and the Isle of Man constitute a common travel area for which passports are not needed).
Although Denmark has signed the Schengen Agreement, it can choose within the EU framework whether or not to apply any new decision taken under the agreement." For more information, lok here:
http://europa.eu.int/comm/justice_home/fsj/freetravel/fronti ers/wai/fsj_freetravel_schengen_en.htm