I´m not a big movie freak and own only a dozen DVD (mainly related to music), but two are Criterions:
- Down by Law (Jim Jarmusch, 1986)
- Solaris (Andrej Tarkovsky, 1972)
Down by Law has been one of my favourite movies since I first saw it. For Europeans, this has a very appealing "deep america" atmosphere, and Tom Waits and Roberto Benigni are great actors (John Lurie is so so).
Solaris is of course much different, I've seen it once and have to go back to it, it's very complex, new things to dicover every time.