My recommendations (in no particular preference order):
1.) "Momo", by Michael Ende. Like another commenter, I wish I'd read this one younger.
2.) "The Neverending Story", also by Michael Ende. The novel (which was originally written in German, but the English translation I have seems decent enough) is far more complex and interesting than the movie, and I suspect a fair number of people on here would find the "world-building" sequences quite compelling. There's a lot in the novel (again, which doesn't translate through to the movie) that goes deeply into questions of what it actually means to be happy, how one might actually make others happy, and what the consequences (both positive and negative) can be of enacting wishes.
3.) The "His Dark Materials" trilogy. Yet another one I wish I'd read when younger (I actually only read these recently).
4.) "A Wrinkle in Time" (along with "A Wind In The Door" and "A Swiftly Tilting Planet"), by Madeleine L'Engle. These I did read as a youngster, and while they do occasionally invoke a certain amount of Christian imagery, it's not nearly as heavy-handedly done as it is in, say, C.S. Lewis' works.
"Wrinkle" was especially dear to me growing up as the main character a socially awkward female math nerd (which is highly unusual for a book written in the 1960s).
And some of the other books, notably "A Swiftly Tilting Planet", did actually help me in terms of being able to seriously question religious dogma, as there's a plot-thread involving a villainous pastor and at the time I read that (around age 12) I was kind of shocked by it initially but then started realizing how a lot of evil in the real world probably stemmed from indiscriminate application of dogma.
I also liked that the books portrayed, in general, the science and math folks as being the good guys, and indicated that trying to understand reality was not a bad thing and did not make people cold or evil.
4.) "The Dark is Rising Sequence", by Susan Cooper. Major thing absorbed from this series: sometimes even "good guys" do things that sound and appear awful. This doesn't mean one has to blindly agree with them, but it does mean that sometimes when there are two major opposing forces, you can't always just figure that throwing in your lot with one of them is going to preserve all your dearest values.
I enthusiastically second #1 & #2 above.
The very best part of Ende's fiction, in my opinion, is his examination of the difference between belief and knowledge. Bastian believes that all sorts of things are good and desirable, but when he enacts his will, he finds that he does nothing but harm.
The theme of skepticism - especially skepticism about what is good, evil, and necessary - is immensely important, and it's one of the key themes of The Neverending Story.
Follow-up To: On the Care and Feeding of Young Rationalists
Related on OB: Formative Youth
Eliezer suspects he may have chosen an altruistic life because of Thundercats.
Nominull thinks his path to truth-seeking might have been lit by Asimov's Robot stories.
PhilGoetz suggests that Ender's Game has warped the psyches of many intelligent people.
For good or ill, we seem to agree that fiction strongly influences the way we grow up, and the people we come to be.
So for those of us with the tremendous task of bringing new sentience into the world, it seems sensible to spend some time thinking about what fictions our charges will be exposed to.
The natural counter-part to this question is, of course, are there any particular fictions, or types of fiction, to which we should avoid exposing our children?
Again, this is a pattern we see more commonly in the religious community -- and the rest of us tend to look on and laugh at the prudery on display. Still, the general idea doesn't seem to be something we can reject out of hand. So far as we can tell, all (currently existing) minds are vulnerable to being hacked, young minds more than others. If we determine that a particular piece of fiction, or a particular kind of fiction, tends to reliably and destructively hack vulnerable minds, that seems a disproportionate consequence for pulling the wrong book off the shelf.
So, what books, what films, what stories would you say affected your childhood for the better? What stories do you wish you had encountered earlier? If there are any members of the Bardic Conspiracy present, what sorts of stories should we start telling? Finally, what stories (if any) should young minds not encounter until they have developed some additional robustness?
ETA: If there are particular stories which you think the (adult) members of the community would benefit from, please feel free to share these as well.
ETA2: My wildly optimistic best-case scenario for this post would be someone actually writing a rationalist children's story in the comments thread.
ETA3: On second thought, this edit has become its own post.