I often (but not always) enjoy films with ambiguous endings that force the audience members to draw their own conclusions on what really happened. Sometimes I think it is satisfying and intriguing, and other times I judge it as a cop out because the author couldn’t think of how to wrap it up (I even caught MYSELF doing this in a couple of stories I wrote years ago in my younger days; that is, I couldn’t figure out a way to have a satisfying conclusion so I wrote a pseudo ending to hide behind the fact that there was no answer to the problem).
Movies where I think the ambiguous ending worked:
“Doubt”
“The White Ribbon”
“Murder By Death” (although I know this ending was played for laughs).
Movies where I think it failed:
“Picnic At Hanging Rock” (although this film is far superior to “Blair Witch Project”)
“Chan Is Missing”
“Absence Of Malice” (although it’s been years since I’ve seen it).
“The Birds”
So what are movies with ambiguous endings that the SDMB members feel “worked well” and what movies with ambiguous endings the people here feel “failed” and why?
Lost in Translation
A Serious Man
The Wrestler
Inception
I think all of the above worked well.
One that I don’t think worked well was Broken Flowers. I enjoyed the film but the ending was pretty disappointing.
Memento, worked very well.
Inception, beyond brilliant.
Drawing a total blank on others I know are hovering in my forebrain.
Look out folks, here we go. 
I don’t think Inception is meant to be ambiguous. The top wobbles and this is not something subjective; they even added the sound effect of its wobble. It ends looking like it will be ambiguous, but I think you were supposed to hold your breath, start groaning(and forehead slapping) at the imminent ambiguity, but then smile when the top wobbles and the director reveals the happy ending.
But perhaps that deserves its own thread.
Note that the wobbling top proves nothing. That could be a dream, too.
Though I have a preference, the final scene in 12 Monkeys can be read in different ways.
There’s a lot of ambiguity in the final shot of City Lights.
Total Recall (the original; haven’t seen the new one)
Twelve Monkeys. 100-post discussion of what the ending means here.
John Carpenter’s The Thing
John Sayles’ Limbo
The ending of Inception wasn’t ambiguous at all. The real ending was that he walked away from the spinning top. That’s the end of the movie. He didn’t care anymore whether he was in “reality” or “dream world” and he accepted where he was and was happy. Reality is what you accept it to be. That was the point.
K-Pax: Kind of a dumb “ambiguous” ending and it really doesn’t make sense that he’s an alien OR a human. Too many inconsistencies.
Blade Runner. I’m of the “Deckert was a replicant” school, but you’ll get a vigorous debate about it.
I don’t recall the ending being ambiguous.
Life of Pi as a recent candidate?
Cast Away?
I thought it worked, although it was a clear setup for Cast Away II, The Return of Wilson.
Safety Not Guaranteed
Not a perfect movie IMO, the secondary romantic plot went nowhere and seemed pointless, but the main one kept me guessing all the through ie is the guy a deluded loser or has he really made a time machine?
Then at the end you still don’t really know for sure. But you can assume what you want 
“Unfaithful”
Did he turn himself in, or did they run off?
I too think the ending of Lost in Translation was well done.
Just what did he say to her? But in spite of the frustration of never really knowing, I think it is ultimately more satisfying this way; each viewer can come up with their own idea that best suits them. The main thing is, she smiled – so it was good.
Regarding Castaway, that is the one film I’ve seen that I think was perfect.
I don’t mean that it is my favorite film; it’s just one that is so well done, I can’t think of anything about it I’d change.
It includes unexpected twists along the way, and yet still completes itself as a perfect circle.