Some time ago, I found this list of REU programs held in 2009.
The main aspects that characterize such programs are: (a) a great deal of lectures on specific topics; and, admittedly more importantly, (b) the chance to gain some hands-on experience with research projects.
I think that these programs are extremely interesting and are precious opportunities for undergraduates to gain a deeper understanding of specific mathematical topics as well as of the "work of the mathematical researcher".
One should note, however, that most of these programs (if not all of them) are not open to European citizens (or, at least, in general non-American applicants do not receive funding).
Q: So, I would really like to hear if you know any similar programs. More specifically, I would like to know there are any such programs outside the U.S. (or any programs in the U.S. that accept also non-American applicants).
Remark 1: A similar question was asked on Mathematics Stack Exchange.
Remark 2: Both questions have been updated in 2015. It would be nice to receive some answers which are up-to-date.