However, an increasing number of rules and regulations are being put in place that will slowly but absolutely change that.
There have been agreements to extradite citizens to other EU countries if they are suspected of committing various crimes. The list of crimes is long and includes fraud and theft.
More recently, EU Justice Ministers agreed their countries would collect fines for one another so there is no hiding place in Europe for those who break speed limits or park illegally.
However, now another more radical step is about to be taken that will bring the security issue home to all Europe's citizens the introduction of new passports.
There is no single EU passport as the member countries could not agree on introducing one a few years ago. Instead they agreed that each country's passport would follow much the same format, giving information in much the same order.
This is still the case. However, following a demand by the United States to carry additional information on passports, and the desire by the prime ministers of the EU member countries to tighten up border security, it has been proposed that microchips be carried in passports of EU citizens.
The chip will contain so called biometric data fingerprints, eye-scans or DNA information on the passport holder. The aim is to make forgery of passports almost impossible. It will also tie in nicely with a coordinated EU-wide system to track people as they travel.
For most Europeans it will come into effect when they leave the EU but for Irish and British people the passport is still required when leaving the country because both countries opted out of the Schengen Europe without borders arrangement.
The chip will have space on it for additional information also but as yet no decisions have been taken on what information could be added.
The biometric information will be logged into the EU visa information system being developed which will operate at all passport control points into the EU and link them all.
At the EU summit in Greece last week, the leaders gave their agreement to the biometric identifiers for passports, visas issued to people visiting the EU and documents for refugees and people with permission to remain in an EU country. The leaders have asked the Commission to draw up a plan of how to implement the proposals.
The Unites States has said EU citizens without biometric identifiers in their passports from October 2004 will have to apply for a visa on which they must include the information required on the microchip.
Biometrics were introduced by the United States as part of their enhanced border security structures following the September 11 attacks on New York and Washington.
Britain pushed the project at the G8 meeting in France earlier this month and said it intends to have the identifiers in all passports by 2006.
Implementing the passport proposals will not be cheap. The EU leaders agreed to spend an initial €140 million on the development of the system but it is expected to cost much more than that.
Costs in the US have been estimated at $3.8 billion for the nine million visas they issue each year. However, the final bill could be close to $12bn.
Civil rights watchdog groups like Statewatch are concerned about the microchip proposal because they see it as a further encroachment on people's liberty. All cross border movements can be tracked using the chip in the passport Statewatch said it is also concerned that there has been no debate at all in countries across Europe about adopting the biometric identifiers.