I play fast and loose with the label of "noir," which is why Liebestraum is on the list.
I hate writing straight summaries, so I'm stealing this one verbatim from IMDB: "Two affairs, a generation apart. Nick, a professor of architecture in upstate New York, comes to an Illinois town to be with his birth mother in the final days of her illness; he was adopted and has never known her. On the first day, he runs into Paul, a college friend, whose construction company is demolishing an old, downtown department store where a murder-suicide happened 30 years' before. The building is of beautiful cast-iron construction, so Nick wants to study it before the demolition. Paul introduces Nick to his wife, Jane, and over the next four days, their attraction grows as Nick explores the old building, attends his mother's bedside, and unravels the past." (Thanks, unknown summary writer!)
I should make clear that I don't think this is a great film - it definitely has its faults. But it is artful, almost hypnotic. It has some Lynchian touches (the very strange brothel scene reeks of it), and a lot more distinctly noir touches, including twisted affairs of both past and present, and deadly jealousies. The entire effect of the film is an unsettling one. Chances are you won't wholly like it (although you may wholly dislike it), but it will attract you against your will. And, really, what's more noir than that?
Extras: the lead character is played by Kevin Anderson, a rather fine actor who also starred in one of my personal favorites, Eye of God - although you may remember him better with Julia Roberts in Sleeping with the Enemy. Plus - if unsettling movies are your cup of tea, Liebestraum's director Mike Figgis also directed 1999's The Loss of Sexual Innocence, which is a thoroughly continental, arthouse type of film that I can describe no better than "unsettling." In fact, if you have any sexual hangups whatsoever, you should probably avoid Figgis's films, including Liebestraum, altogether. They will not help.