It involves more than 4,000 higher education institutions in 31 countries, has been running for 22 years and has just celebrated the participation of its 2 millionth student.
But Erasmus, the European Commission's flagship overseas-study programme, could be in danger of missing its targets despite student mobility now being at the heart of Europe's education agenda.
At a conference at Lund University, Sweden, earlier this month, Maros Sefcovic, the European Commissioner for Education, stressed the importance of Erasmus to Europe's competitiveness.
"In today's world, one's personal and professional success in life is all about having the right skills mix. I'm convinced that mobility programmes such as Erasmus are part of the answer to equipping people with the skills required in a complex world."
But he said that participating numbers were not high enough and warned of a "worrying" decrease in some countries.
Since the programme was set up in 1987, the number of Erasmus students has increased from just 3,200 students to about 162,000, and there has been healthy growth in many countries recently, including the UK (see graphic above right).
But Mr Sefcovic said that Erasmus covers only about 3 to 4 per cent of Europe's student population.
"We need to substantially boost mobility numbers to better spread the benefits among students," he added.
The Commission has a target to reach 3 million Erasmus students by 2012.
"Can we reach our target" Mr Sefcovic asked. "It will be a challenge. We have seen that in ten countries the number of outgoing students has decreased, sometimes by more than 10 per cent. This is a worrying trend."
Sofia Larsen, chair of Sweden's Parliamentary Committee on Education, said: "The number of Swedish students participating has decreased steadily, from about 3,300 students ten years ago to approximately 2,300 students today.
"Only 14 per cent of students have studied abroad during their course of study. In my opinion, this figure is far too low."
The UK saw a 42 per cent increase in outgoing Erasmus students between 2006-07 and 2007-08, from 7,235 to 10,8, following the programme's introduction of work placements.
The Europe and Globalisation Directorate of the Foreign and Commonwealth Office said there was 6 per cent growth in 2008-09 in UK take-up, and added that the number of applications for 2009-10 is "looking encouraging".
The Lund conference, "Erasmus - The way forward and the Green Paper on mobility of young people", discussed ways to dismantle barriers to student mobility, outlined in the Commission's Green Paper, Promoting the Learning Mobility of Young People.
Mr Sefcovic said that the first challenge was money, arguing that "governments need to resist the temptation to cut their budgets for schools, universities and research" in the difficult financial climate.
"We will need a steep increase in resources at all levels if we are to finance our ambitious mobility agenda," he said.
He also called for long-term investment in foreign-language teaching, plus improved information and communication.