The French title (from the original trailer) is "The Man Who Wanted To Know". I suppose this sounds a bit vague for American audiences, hence "The Vanishing", which puts a bit of mystery into it.
Others have pretty much covered the plot (and at least one a-hole gave away the ending), so I will not repeat it.
I found the movie interesting, and even when you know "who dunnit" early on, you still don't know how he did it till the very end. I consider this more of a "psychological drama" than a "horror" film in a Friday the 13th mode. There is no blood or things popping out of shadows.
The ending is creepy, no doubt, but it also seems to be quite logical in the overall scheme of things. The disconcerting part, beyond the outcome however, is the rather non-chalant attitude of the bad guy through out the movie and particularly the very last scene. We never really know what the root of his problem is, but I suppose it is not necessary.
For a Criterion Collection DVD, there are very few "extras". A trailer (which does not count), required subtitles in a couple languages, and a 2-page written review. The liner notes tell us this is a new digital transfer (looks good) and the soundtrack was mastered from a 35mm magnetic track (sounded OK to me).
Not for everyone, but I'm giving it 3 stars overall - slightly better than average - based on 4-star movie/2-star extras and relatively high price.