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Two movies that fit the catagory 'Science Fiction' that weren't special effects or action films, but I always thought were well thought out science fiction plots:
Colossus the Forbin Project
The Andromeda Strain
I especially liked Colossus because of all of the 60's 'computer taking over the world plots' on TV shows and movies, which were all were defeated by asking the computer some vague question like 'why' or 'compute Pi to the last digit'.
---someday something witty will be placed here----
Colossus had some interesting ideas. It and the Soviet computer communicated starting with simple math and developing their own undecipherable language. And at the end it appears that its only goal is to prevent war, but we don't see where the line between war and any violence is.
What happens next, assuming the computer is unbeatable, would make an interesting SF novel. Or maybe it leads to ST:tOS?
I think the ambiguous ending is part of reason why most people have never seen or even heard of it. It's not a triumphant 'man over machine' ending that is very common even today, and we never find out what ultimately happened to humanity in general or Forbin in particular.
The reason Arthur and Ford were cast into space by the Vogons: Adams thought the radio series was being cancelled, so he killed the characters off in what he thought was the last episode. He was wrong, and needed to bring the characters back. The result: Infinite Improbability Drive.
Akira was hugely influential, but I found it to be a snoozefest.
Royal Space Force: The Wings of Honnêamise (1987), while not popular in Japan, is worth a watch. It's about the first space launch on an alternate Earth- pretty much "The Wrong Stuff" because the effort has no prestige and the government expects it to fail.