The Departed (absolute finality) and No Country For Old Men (ambiguity).
I thought No Country For Old Men was really good until they just decided to quit writing and rolled credits. Weirdest ending I've seen.
I would have to say Sling Blade. Incredibley realistic in every aspect!!;)
Definitely would have to be "The Departed". One of the best movies I have ever seen.
The House of Flying Daggers
I think "The Family Man" is a really good movie. You don't know if it's a happy ending or not
Casablanca, hands down. With honorable mention to Cannonball Run. Everyone knows the traditional happy ending would have been Dean and Sammy winning the race.
Cool Hand Luke.
Hands down.
Have seen a lot of great flicks mentioned here...but for me..."Being There"
Some great movies without happy endings are Only God Forgives, Kids, Gerry, Last Days, Elephant, this is england, Made in Britain just to name a few.
The Wicker Man (1973) - I haven't seen the more recent version starring Nicholas Cage.
Anna Karenina (1948)
Nicholas and Alexandra (1971)
Brief Encounter (1945)
Brazil (1985)
A Tale of Two Cities (1958)
Arlington Road
Atonement
Colossus - The Forbin Project
Cabin in the Woods the 2011 edition
The Girl with the Dragon Tattoo. Knowing that it's not a perfect ending but hoping they make movies for the other two books :P