The cost is 1o euros per year, and in addition to music and videos a library patron can check out ebooks. The library offers 7,000 ebook titles at the moment, and they can be checked out for 2 weeks. Audiobooks, music, and videos can be checked out for a week, and digital magazines can be checked out for a day.
This isn't the first program of its kind, though it is probably the most open. I know that several public libraries here in the US, including the NYPL, let non-residents get library cards. An NYPL card, for example, is free to anyone who lives in or pays income tax to the state of New York. I was also under the impression that those outside the state could also get a card, but that doesn't seem to be the case. And while the NYPL offer is cheaper it is also limited to a smaller population. The state of New York has around 20 million residents, while Germany's population is around 82 million.
There are also similar commercial programs in a number of countries, including Mofibo and RiidrOne in Denmark, Madrid-based 24Symbols (Spanish language focus but with some English language ebooks), various niche services like Safari Online, and of course the Kindle Owners Lending Library.