The European Commission wants people to have the right to health care across the EU if they are entitled to receive it in their own country.
Here, BBC correspondents provide a snapshot of health care in six European countries, for the citizens who travel abroad and the foreigners who come for treatment.
1. UK: NICK TRIGGLE
Those travelling across the EU for treatment have increasingly included Britons stuck on waiting lists for treatment at home.
After the government announced in 2001 that patients facing "undue delay" could head abroad for treatment - a reversal of a longstanding policy limiting overseas treatment to exceptional circumstances - figures show 1,000 people took advantage.
While the agreement of local health authorities was required, the trend continued until waiting lists in the UK were brought under control.
Last year, the figure stood at just over 350.
But the judgements of health chiefs working for primary care trusts have not always been met with agreement.
The case of Yvonne Watts - partly responsible for triggering the latest EU plan - rested on the fact that the Bedford pensioner disagreed with her local trust's decision not to fund her treatment.
She ended up going to France for her hip operation, paying out £3,900, and then claiming the money back via a high-profile court case.
But just as patients head overseas for treatment, so patients from overseas head to the NHS.
Last year, there were estimated to be 750 cases where patients from EU countries came to the UK for non-emergency treatment.
These cases, paid for by the individual's home country, have tended to be for specialist care, such as liver transplants.
Critics have attacked both trends. Doctors have expressed concern that paying for treatment abroad sends NHS funding overseas, while other say it is unfair that NHS capacity should be used to treat overseas patients when UK taxpayers face waiting lists.
2. GERMANY: TRISTANA MOORE
According to the German health ministry, less than 1% of German patients travel abroad each year for medical treatment.
There are a few exceptions. For instance, German patients living in a border region may cross over to another country, such as France or Austria, and they are often advised to do so if, for example, a specialist hospital in the neighbouring country is closer to them than a comparable one in Germany.
Germans take a pragmatic approach to cross-border medical care
When they do travel, it is often for dental care (where patient co-payment is fairly high) - so Germans tend to travel to countries where dental care is cheaper, such as Hungary.
Because Germany has a reputation for high-quality hospital care, including extensive outpatient services, and waiting lists for operations are virtually unheard-of, there is usually no reason for patients to go elsewhere.
German health services provide treatment for patients from other EU countries, especially in the border regions.
There are some advanced models of cross-border cooperation in specialist hospital care, for example, between Aachen in Germany and Maastricht in the Netherlands.
The cross-border provision of health care is not a controversial issue in Germany. Germans tend to take a pragmatic approach.
If German patients cannot get the necessary treatment at home without undue delay, then the authorities tend to welcome the fact that patients would travel to foreign hospitals.
3. CZECH REPUBLIC: ROB CAMERON
Few Czechs seek treatment elsewhere in the EU, using instead the comprehensive Czech health care system.
A small number of patients, however, go abroad for highly specialised treatment unavailable at home.
The Czech Republic is obliged to provide the same medical treatment to EU citizens as Czech citizens, providing they offer proof of insurance.
EU citizens who work or live in the country are required to make payments to the state health insurance company VZP.
According to the Czech health ministry, there has been no noticeable influx of EU health tourists seeking treatment from Czech doctors, although as the ministry's spokesman pointed out "the doctors don't exactly advertise their services either".
The exception is plastic surgery - Czech plastic surgeons are highly regarded and operations are far cheaper than in Western Europe. However, this treatment is private and not covered under primary health insurance.
There is little opposition to providing care to other EU citizens because the Czech system is not being "abused" by them.
A much larger problem, according to the Czech health ministry, is posed by non-EU workers who require hospital treatment but lack adequate insurance.
"If a Ukrainian labourer falls off a piece of scaffolding we treat him - we don't check whether his health insurance is valid first," said the spokesman.
Many such workers are uninsured, and the Czech healthcare system is left to pick up the bill.
4. SPAIN: MARIAN HENS
Very few Spaniards now travel abroad for health care, reversing the trend from a decade ago.
The change is largely due to the availability of abortions inside the country and the burgeoning medical tourism industry.
Patients from all around Europe arrive in the Mediterranean nation to take advantage of Spain's "universal" health system and have complex specialised operations free of charge.
Spain now attracts a different kind of "tourist"
Knee or hip replacement, cardiac and eye surgery top the list, but fertility treatment and cosmetic surgery are increasingly popular.
Health tourists from the UK, France, Germany and Holland are the most regular visitors, an inflow which is putting the Spanish health system under unprecedented strain.
The Nurses' Union, SATSE, has repeatedly complained that if health tourism is not controlled, it could end up making Spain's public health service collapse.
But it is not only medical tourists that concern Spanish health professionals. The high numbers of EU pensioners that live in Spain - especially the British - are also burdening the Spanish welfare state with millions of euros of medical costs.
In response, the Spanish authorities have been seeking compensation in Brussels, but so far Spain has only recovered a fraction of what it has spent in treating other EU nationals.
5. ITALY: CHRISTIAN FRASER
The number of Italians seeking medical care abroad is in decline, according to government statistics.
In 2005, just 5,000 people sought help in neighbouring countries, down from 20,000 in 1995.
Those who do travel - mainly to France and Germany - do so to avoid waiting lists for elective surgery or to benefit from specialist cancer care or heart surgery.
In a recent European survey, carried out by the French pollsters CSA, 68% of Italians said they would consider travelling abroad for surgery not available at home.
And it seems there is very little opposition to foreign patients coming to Italy - providing they pay their way.
Of those surveyed, 70% said they would welcome foreigners as paying patients.
There is a sizeable private sector in Italy which caters for them, most notably in areas of fertility treatment and cosmetic surgery.
But the standard of care in Italy varies widely between the prosperous north - where care is comparable with most European countries - and southern cities like Naples, where the health service is considered to be weaker.
The exception to that rule is the European transplant centre in Palermo, a public-private partnership with the University of Pittsburgh, which attracts a number of foreign patients.
The centre performs liver, kidney, heart, lung and pancreas transplants, and is widely considered a European leader in organ transplants.
6. IRELAND: DIARMAID FLEMING
The Irish public health service is widely perceived as an outdated system struggling to provide the levels of care demanded by a country with the fastest-growing population in the EU.
A programme of modernisation is under way, but officials agree that the existing system does not attract residents of other EU states seeking care.
Ireland is trying to bring its health care up to European standards
Loosely based on the NHS, the Irish system is, however, only free to holders of medical cards granted to the poor, those on welfare and all those over 70.
All EU nationals legally resident in Ireland are entitled to apply for a medical card but are also subject to a strict means test.
A visit to a doctor's surgery costs roughly 50 euros (£35), while a trip to Accident and Emergency costs 60 euros (£42).
For those with the EHIC, held by EU citizens visiting Ireland, a visit to most doctors is free, as is subsequent specialist treatment if deemed necessary by the doctor.
About 100 Irish patients each year are sent abroad for specialist treatment, usually for cancer care, cardiology or neurology services. They usually travel to France, Belgium, Sweden or the UK.
Many thousands more travel for private dental care, mainly to Hungary.
The Republic and Northern Ireland have already sought to pool health service resources with a pilot programme to give cross-border GP coverage for out-of-hours care.
Launched in 2006, the first phase of the project provided access for residents of the remote Irish region of Inishowen, Co Donegal, to doctors in Londonderry over the border in Northern Ireland.
In November 2007, health authorities announced that a reciprocal programme would give residents of south Armagh cross-border care options.
In emergencies, patients have been treated across the border in either Northern Ireland or the Republic when treatment has not been available in their own jurisdiction.