It was interesting to see that a couple of others have already mentioned a film that I think is really moving:- The Apartment, @Graphista and @Helocariad. A very moving film, especially at the end, the look on Shirley MacLaine's face when she hears what she thinks is a gunshot.
I'd like to add one more though, a film from 1972 called Silent Running that I first saw on TV in the late 70s. This is the film that got me thinking seriously about the environment right back then and ever since. So, to that extent, it really did have a profound effect on me in that it changed my lifelong outlook on life.
It's really not like many of the other films that have been mentioned here (apart from perhaps Solaris) but it is worth seeing. If you ever listen to Mark Kermode he's described it as:-
"one of my all time favourite movies and one of the greatest sci fi films ever"
and this is the review from the Guardian:-
This authentic 1970s cult sci-fi classic stars a key figure of the period, patrician hippie Bruce Dern, as an idealistic crew member of a 21st-century space station refusing to destroy the only forest vegetation saved from a defoliated Earth. The screenplay by Deric Washburn and Michael Cimino (later to collaborate on The Deer Hunter) and Steven Bochco (of subsequent Hill Street Blues fame) delivers its ecological message with humour and imagination, and Joan Baez sings the appropriate songs. But this deeply moving, immaculately staged film is essentially the work of Douglas Trumbull, only 28 at the time, a special effects expert who got the assignment after making a major contribution to Kubrick's 2001: A Space Odyssey
www.theguardian.com/film/2011/nov/27/silent-running-french-classic-dvd