Noi Albinoi, although it's rather a dark comedy/drama, and not as brooding and disturbing as The Reflecting Skin.
~
Everyone is unique, except for me
~

i'd recommend the finnish movie 'muukalainen'
http://www.imdb.com/title/tt0969307

As a couple of others mentioned, Northfork is a film that contains the same wonderful cinematography (shot in Montana) as well as quirky/disturbing characters.
One film that has not been mentioned is Angela, which is similar in that the young character exhibits disturbing behavior fueled by external sources (in this case religion rather than comics). The setting is not spectacular but it does contain some wonderful imagery nonetheless. Don't miss this one.
http://www.imdb.com/board/10112364/combined

Well, recently there was The White Ribbon, I know The Devil's Backbone was mentioned, which I thought of right away, along with The Other (very creepy). The Gift (2000) reminds me of Reflecting Skin a bit, Wise Blood was another great suggestion. Definately check out The Ratcatcher (1999), one of the most disturbing (and truthful) films about childhood. You'll never forget "Snowball went to the Moon."

This message has been deleted.

http://www.imdb.com/board/10454792/
"Bubble"
In the same spirit.. originality.
I love this movie the same as "The Reflecting Skin" and "Gummo." (The way good parents love each of their children)
The "cast" was basically pulled off the "street" in the town of Ohio where it
was filmed. Mostly hand-held, digital filming with natural light only - it is visually stunning.
(The bonus material for me was essential - I sort of wished I'd viewed it before the film - don't skip it)

"Around the Bend" - Michael Caine and Christopher Walken, you feel the New Mexico landscape
http://us.imdb.com/board/10384810/
"Erndira" - Mexican film, great and disturbing story set in strange Mexican landscape
http://us.imdb.com/board/10085501/
"A little old lady got mutilated late last night Werewolves of London again."

For some reason Dead Man's Shoes come to mind.
Not exactly as much a focus on the landscape but it has a quiet intensity and takes place in a small country village.
http://imdb.com/board/10419677/

Picnic at Hanging Rock

Boy, you've received so many responses, but I've two other films not mentioned - CLEAN SHAVEN & BUTTERFLY KISS, the themes are different but the disturbing tone is similar. Both stay with you long after viewing.

Spanish film called
Spirit of the Beehive
is kinda like this, but much more subtle and brooding rather than blaring, obvious and parodic.
Bad Boy Bubby
is a total hoot, no less perverse and removed from the world we know than Reflecting Skin, but quite a bit more restrained and honest as well.
In a Glass Cage
is another Spanish film. Dark, sadistic, brimming with horror and wickedness, but too misanthropic for my taste.
Joshua
is a new film that premiered at Sundance about a very twisted boy. It teeters giddily on the edge of uncomfortable, comical weirdness but has a more typical 'slasher' denouement.

Olivier Olivier didn't really remind me of The Reflecting Skin, not in plot anyway. When the brother and sister are playing the trick on the neighbor in the beginning, yeah, that kind of made me think of The Reflecting Skin. And the fact that both involved child rape and murder.

There is a French movie called
Olivier, Olivier
(1992) that strongly reminded me of this one. Highly recommended!

The Devil's Backbone (2001) Guillermo Del Toro
(I'm surprised no one has mentioned this film yet. Very creepy and beatiful)
Badlands (1973) Terrence Malick
(Highly underrated crime drama similar to Bonnie & Clyde and Natural Born Killers. Not bizarre, but has atmospheric dreamlike cinematography. The scenery reminded me of "The Reflecting Skin".
Valerie and her Week of Wonders (1970) Jaromil Jires
(Awesome Dark Czech Fairy Tale)
Kytice (2000) (aka. wild flowers)
(Another extremly dark Czech folk lore movie)
(available at www.superhappyfun.com)
Swallowtail Butterfly (1996)
(Awesome Japanese coming of age drama. Like City of God meets Kids)
(also available at www.superhappyfun.com)
Was "City of God" mentioned yet?

New Gilliam movie: Tideland.

You should try "Fists in the pocket" http://www.imdb.com/title/tt0059619

The only issues of Jack Be Nimble on DVD are OOP pan&scan releases in the US and Spain. I wouldn't compare it to Reflecting Skin at all, but it's a creepy movie well worth checking out.

I love Afraid of the Dark! In fact, I love a lot of the movies mentioned and am now going to look for a few of the others.
I haven't seen the Reflecting Skin in over 10 years, but the first movie that came to mind was Jack Be Nimble with Alexis Arquette. Amazing film. So worth checking out. Not sure if it's on DVD though.
Amanda By Night

These two films use more claustrophobic settings that mirror the children's somewhat distorted perspectives: (I don't see that anyone has mentioned these, so forgive the redundancy if I missed a post that included them) "Afraid of the Dark", and "Careful, He Might Hear You".

Michael Tolkin's "THE RAPTURE"

Viva La Muerte (1970) Fernando Arrabal
(All about a little boy groing up in Franco era Spain, and his surreal psychadelic nightmares)

It warms my heart to see that this thread (that I started two years ago) lives on, with serious recommendations and a good discussion.
Thank you all!!!
Of the latest recommendations
Vigil, Tideland (Gilliam), Northfolk, Wicker Man, Parents, Secret Rapture and Lolo
are all films I haven't seen.
Tideland and Secret Rapture are the only ones I had heard of before, and thanks to you lot I have now heard of the rest and have something to look for, or will recognize if I stumble upon a mentioned title in the video store or on tv.
It's nice that some of these films and others earlier mentioned take a grip on the comic side of childhood and other miserable subjects. I could see more of good films that bring up the (necessary?) tension between seriousness and humour.
Some good films that could suit on this thread are (with very few opportunities for laughter, though):
The Return (Vozvrashcheniye)
http://www.imdb.com/board/10376968/
One of those films that creates an almost meditative concentration with the viewer. The film has a very good story.
The Quiet Room
http://www.imdb.com/board/10117422/
By Rolf de Heer who also made the wonderful Alexandra's Project (and eh, Bad Boy Bubby)
Lilja 4-ever
http://www.imdb.com/board/10300140/
An uncompromising film filled with rage and sadness, one of the most important films I have ever seen.

Watch a film called "Leolo", I'm sure you will enjoy it just as much. Let me know?

The Secret Rapture. Depresso-Beautiful.