Non-theist cinema?

Some atheistic films not mentioned in the OP:

Agora, Bad Boy Bubby, Chocolat, Inherit the Wind, The Ledge, The Wicker Man, Planet of the Apes, The Magdalene Sisters, There Will Be Blood, The Tree of Life, The Golden Compass, The Apostle, Black Robe, Breaking the Waves, Creation (about Darwin), The Crucible, Contact, Hanna and Her Sisters, Paul, Saved, Whatever Works, The White Ribbon, God on Trial, Watchmen.

Toy Story

Toy Story, you see, is a tale of coming to terms with atheism. It's an atheist allegory. Buzz Lightyear, of course, is a member of the dominant group (the masses of identical Buzz Lightyears) who fervently and insistently believes that he is in intimate contact with a higher power -- Star Command (namely, God). Woody, the atheist, spends the duration of the movie trying to convince Buzz that Star Command not only isn't real, but does not communicate with him. Instead of Star Command, Woody advocates that Buzz believe in other people (Andy) who he should focus on interacting with rather than a non-existent higher power. When Buzz finally does realize that Star Command doesn't exist and that he is just a toy, he becomes deeply depressed until Woody points out the wonderful nature of life and that he can derive as much meaning from being a meaningless toy as he did from being under the control of Star Command.

The Dark Knight is essentially a film about morality, including textbook trolley scenarios, tests of individual integrity and the relation with the state, etc. The Joker argues that all plans, all goals and life in general is meaningless and the other characters disagree. But at no point do they say "the joker is clearly wrong because God has a plan, and killing people is innately bad because God says so." This perhaps makes it one of the best discussions of non-theistic morality in popular culture.

Not quite what you were getting at, but I liked "The Religion Episode" of Glee (I cannot in good conscience suggest it to someone who didn't already enjoy Glee, at least as a guilty pleasure, although I do think it's a reasonable stand-alone episode).

The episode made some effort to be balanced (including a similar "it's okay to have religion as long as you're not too crazy." But the central emotional issue is about an atheist kid whose dad is dying, and how he copes with it. Notable things about the episode include:

1) It generally gives more weight to the atheist than religious arguments (both in a scene where actual arguments are presented, and in general tone)

2) It is interesting that the atheist character is gay, and has already come out and is proud of it, but the situation with his father forces him to "come out" as an atheist, when people start offering him prayers and other well-intended religious comfort.

3) The climax does not involve the inherently negative idea of "God doesn't exist," but rather "My relationship with my father is sacred, for its own sake."

4) The series' antagonist turns out to be an atheist. At first this looks like they're going to pull an Evil Atheist thing. But as it turns out, being an atheist is Sue Sylvester's single most positive trait. She's an atheist because she prayed for her down-syndrome sister to get "better", which never happened, and eventually concluded that she lived in a world beyond the reach of God. But she has a good relationship with her sister. And she ends up being fairly reasonable in her interactions with the religious characters. She's told "Don't shove your atheism in our face," and her response is "fine, but don't shove your religion in mine."

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And there's the My Little Pony episodes on curses and bayesian updating.

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An alternate approach you can take is to look for fantasy movies where there are gods, but they're treated more like Sufficiently Advanced Wizards, because they actually, demonstrably exist. There's not a whole lot of difference between that sort of setting and a completely non-theistic one.

I'm having some trouble thinking of movies like that, though. I can think of books, like the Discworld series or most books set in a Dungeons and Dragons setting. I can think of webcomics, like Errant Story. I can think of a fair amount of anime and manga. The Stargate franchise definitely counts, and has a few movies (albeit mostly direct-to-DVD). I'm drawing a blank on movies, though.

(Come to think of it, Stargate SG-1 might count as straight-up atheistic; the "gods" are all godlike aliens on a megalomaniacal power-trip, and in one of the later seasons, the main villains are the gods of a religion that looks remarkably similar to Christianity in one of its violent old-school variants.)

The lack of religion was what cued me in to the ending in The Village.

Ikiru, Tokyo Story, The Diving Bell and the Butterfly, Goodbye Solo. Not sure how well those apply to your criteria--it's been a while since I last saw them. I would search through South Korean, Japanese, and European cinema because they're more likely to have what you're looking for.

Edit: Wow, I completely forgot about Ingmar Bergman. His movies are exactly what you're looking for. The Seventh Seal and Wild Strawberries are classics.

I always felt that the movie "A Serious Man" was non-theist. The main characters are all Jewish, but the story itself (how he fails to find meaning in the answers given to him by the rabbis, the constant stream of bad things happening to him despite his good nature) points to a world in which there is not a loving God looking out for his own.

I would recommend watching it, as it is a sad yet poignant movie.

What about The Truman Show ? It pretty much explicitly destroys several religious tropes.

Gratuitous plug: I wrote a blog entry on this subject a while ago. This is part of a much more general pattern that popular media reinforces magical and wishful thinking and direct portrays making conclusions based on the evidence as a bad thing.

A most interesting and highly recommended film is Jesus of Montreal. Claimed as "one of ours" by both theists and atheists.

Star Trek V: The Final Frontier.

Nobody said it had to be a good movie. ;)

I liked Frailty. Without giving too much away, it demonstrates how any agent with god-like powers could make you believe whatever it wants you to believe. Therefore if you ever find yourself in a universe in which gods and powerful demons exist and have an interest in influencing your life, you could fall into a situation where you have no means of determining which gods or demons are best aligned with your long-term goals. Also, a sufficiently cogent propaganda campaign could have a good chance of convincing you to commit atrocities.