I, too, am a big fan of "outside-the-box" movies that challenge my way of thinking!!! I'm glad I'm not the only one!
I agree with all of the "thumbs up" for
Mullholland Drive, even though it *was* totally WTF (that's David Lynch for ya). Same for
Requiem for a Dream. And, co-sign with those who gave a "thumbs down" to
Vanilla Sky; I just wasn't feelin' that as one of my WTF films of choice.
Even though it wasn't necessarily obscure,
American Beauty is one of my all-time favorites. 1999 was a good year in film (i.e.
AB,
Magnolia,
Being John Malkovich, etc.).
As far as fairly recent films I've seen are concerned,
Dirty Pretty Things and
Swimming Pool were good. I wasn't feelin'
Eternal Sunshine of the Spotless Mind or
Adaptation (with the exception of Chris Cooper's Oscar-winning performance), both Charlie Kaufman films. I guess they were both just too "out-the-box" for my taste. Another highly-acclaimed film I had mixed feelings on was
The Dreamers. All these critics were saying it was the best thing since sliced bread, and I was just like

. I think they *felt* as though they *had* to praise it since it was a Bertolucci film.
But, there's one obscure film that has resonated with me since I saw it a few years back:
Irreversible. The story runs "backwards" similar to the way
Memento did; it stars real-life couple Monica Bellucci (with whom I share a b-day {Sept. 30}

) and Vincent Cassel (the "Night Fox" character in
Ocean's Twelve). For those not familiar with the plot, check these links out:
http://www.nord-ouest.com/site/irreversible/
http://www.imdb.com/title/tt0290673/
It was very controversial for two scenes in particular; it was reported that many theater patrons walked out due to the graphic nature (I witnessed someone walk out when *I* saw it). But, as a self-proclaimed movie critic, it's been my strong belief that such scenes in movies aren't the "be-all-and-the-end-all" of the entire film, just a part of it (i.e. the infamous sex scene in
Monster's Ball; I digress

). It's what people talk about, but it's not the whole story. Just my humble opinion.
At any rate, it's worth checking out, even if you have to turn away when watching those particular scenes.
In general, I'm a big fan of indies, foreign films (namely French), and certain British comedy (ala
Four Weddings and a Funeral,
Love Actually, etc.). One of my fav places to see these types of movies is back "home" in Alaska at a place called the Bear Tooth (
http://www.beartooththeatre.net/). I've been so deprived living down here.

I can't wait to see some quality films when I go back this summer!!!
PM me or send me a message on Facebook for more!
Thanks again for this thread!!!