Se7en
Dark comedies:
Eating Raoul, thirded
Hot Fuzz
The Ladykillers - both the original and the remake are very good, IMHO, although very different
Psychological thrillers:
In the Line of Fire - Clint Eastwood is great as a Secret Service agent squaring off against a crazy-like-a-fox assassin (John Malkovich)
Notorious - One of Hitchcock’s very best
Se7en, seconded
Second In Bruges, simply amazing.
It’s old and you’ve probably seen it but I love Primal Fear – it’s not funny but it’s probably my favorite psychological thriller.
I watched 36 Hours recently. Interesting premise: James Garner is a WWII staff officer who knows the details of the upcoming D-Day invasion. He’s captured by the Germans. The Gestapo wants to torture him but one German says that he’ll resist torture so it’ll take too long and they’ll have to figure out what information he gives is true. Instead, this German sets up this fake American occupation base in the middle of Germany in order to convince Garner that it’s 1951 and the war is over - so he can talk about D-Day freely now.
(these may be too obvious, but for black comedy)
*Harold and Maude
Wonder Boys
Throw Momma From the Train
Little Miss Sunshine
Fargo*
and psychological thriller,
The Talented Mr. Ripley
psychological thriller:
Final Analysis - with Richard Gere, Kim Basinger, and Uma Thurman. Gere is a psychiatrist who becomes involved with a woman that he’s not sure he can trust.
dark comedy:
Keeping Mum - with Rowan Atkinson, Kristen Scott Thomas, Maggie Smith, and Patrick Swayze. An English country pastor is having marital problems, their new nanny has a dark secret, and bad things start happening to some of the locals.
Lots of my all time favorites have already been mentioned in this thread!
Let me recommend some of the early work of John Dahl: “Red Rock West” and “The Last Seduction.”
Both are about people skirting the edge of the law; good people who are sucked into doing what they know isn’t the best of ideas, but they are desperate. I don’t know if either was *intended *to be funny, but I found them hilarious. And I don’t mean that as an insult; I mean it as high praise in the ability of the director to show the absurdity of life while also showing the tragedy. You laugh so you don’t cry.
ETA: “Rounders,” another John Dahl film, also fits that mold of doing things against your better judgment to tragi-comic effect.
Also - just about anything by David Lynch or the Coen Brothers can count as a dark comedy to me…TRM
ETA again: hmmmm, both Dahl and Lynch hail from Montana. Something in the water?
Hardly anyone I know has seen it, but for dark comedy I love Drop Dead Gorgeous
House of Cards. Recently watched this on a Netflix recommendation, and enjoyed every minute of it.
For what it’s worth, though–it’s not a movie, it’s a series (twelve episodes, across three BBC ‘series’). It’s not primarily a dark comedy–rather, it’s a political thriller. But Francis Urquhart, the main character, has a delightfully dark, wry wit that he frequently shares with the audience. Furthermore, he definitely commits a number of crimes throughout the course of the series. 
It’s absolutely worth it–Ian Richardson as FU is spectacular. I somehow managed to cheer for and against him simultaneously at several points in the show. Check it out.
A classic (that I haven’t seen in years): The Trouble with Harry.
Two dark comedies I’ll recommend:
U-Turn - An Oliver Stone film with a star-studded cast. I never heard of it and rented it once. It will make you laugh out loud.
***Payback ***- One of my favorite Mel Gibson films. And it’s a very funny movie with a ton of quotable lines.
I’ll enthusiastically second Payback (the ad slogan was, “Get ready to root for the bad guy”) and House of Cards (Ian Richardson deserves every acting award on the planet for playing Urquhart, a deliciously evil, ambitious and amoral politico). There are two sequels, also starring Richardson, but IMHO the original is far superior.
I second:
World’s Greatest Dad
Death To Smoochy
Keeping Mum
And I also suggest:
One Hour Photo…It is not a comedy but a creepy…hmmm I hesitate to use the word thriller. It is laid back but so interesting that the pace of the movie is steadily moving forward simply because Robin Williams is so damn good.
I know, four of these movies star Robin Williams, can you tell I’m a fan?
Third on Keeping Mum.
Freeway - dark, messed up, funny as hell. It’s little red riding hood, if red’s mama was a speed whore and the wolf was a serial killer in California. And while I’m suggesting Reece Witherspoon movies, try Election. Also effed up and funny.
Seconded, on both counts.
A Simple Plan. Everybody has a choice, to do the right thing. But only once - after that, they have no more choice.
Regards,
Shodan
However, the main character’s two aunts and his brother are all serial killers, which rather makes up for the lack of crime on the part of the central character.
Worth seeing for Kirsten Dunst’s tap dance alone! 
I don’t know if it counts as a comedy, but Zentropa (a/k/a Europa) is pretty dark, all right, like the whole thought process was, “How dark can we make this? No, darker! Darker!”
Dr. Caligari – no, not the 1920 silent Expressionist classic; the 1989 surreal what the fuck was that?! cult classic.
Oh, and of course, Naked Lunch (dark comedy, psych thriller, works either way).