Dancer in the Dark
The whole film just gets bleaker and bleaker, closing with what has to be the most depressing closing scene in all of cinema. I'm being intentionally vague because you owe it to yourself to watch this one.
Oslo, August 31
Another film with a pretty bleak undercurrent. Yet, despite its subject matter, this closing scene almost has a peace or tranquility to it...like everything that you felt during the movie towards the protagonist was washed away in a sort of cleansing acceptance. Sad, but in a way relieving.
Harold and Maude
The whiplash-inducing "twist" that catalyzes the closing sequence, followed by that sequence itself (with the perfect musical accompaniment of Cat Stevens' "Trouble") is just devastating. I watched this movie 7-10 times in one week after I saw it for the first time. So, so good and an incredible ending.
The Red Shoes
Probably the weakest of this list, but still sticks with you.
Ex Machina
I never put it together, but heard someone mention that the ending is basically Plato's Cave, which makes total sense and adds an incredible amount of depth to that final scene. Plus, I like an ending where things don't go as planned.
Children of Men
Chilling ending to a tense, disparate film.
Frances Ha (shut up)
It adds a perfect little whimsy to what is just a fun flick about your 20s. Finally settles into her own spot after the transitory nature of her character throughout the film. (NYC to Paris to Sacramento to upstate...) Always puts a smile on my face.
Spirited Away
It's just pretty.
Probably more but that's all I can think of on short notice.
[EDIT] Edited in explanations as to why.