My 1st thought
District 9 hasn’t been mentioned yet, so I’ll throw it out there, since it’s the most recent sci-fi film I’d consider to be a classic of the genre.
Re: Dune, it should be noted that there are two adaptations of it that are both noteworthy for different reasons; the Lynch film, and the 2000 Sci-Fi Channel miniseries. The former is better in terms of cinematography, production values, and epic “feel”; the latter is a more faithful adaptation of the source material and covers a lot of the nuances that the film glossed over.
Two with the unforgettable John Agar:
Journey to the Seventh Planet. Scared the hell out of me when I was in second grade. The big Swedish boobies in it are nice too! :o
Zontar, the Thing from Venus. Almost as bad as Plan 9 from Outer Space, which should be on the list too.
Has Time Bandits been mentioned? Watch this one when you’re stoned!
The same goes for Flesh Gordon. 
Yeah, I watched the 60s film a couple of days ago, and still love it, even though it shows many of the flaws that plague its remake. Nostalgia plays a part, but it’s also better crafted; and it doesn’t contradict itself.
There is also a shift in point of views: the core of the 60s version is science, what it can achieve and destroy. Man’s action is the mover of all things.
And while the remake seems to make the same point, we listen to a thesis that implies the presence of another force, whatever that may be, that restricts man’s reach.
However, the actions of the protagonist show us the antithesis, and no synthesis is forthcoming, which means that we are left with a mess.
Very unsatisfying movie.
Before you watch Flesh Gordon, you should watch the 1936 serial Flash Gordon. Otherwise, you will miss a lot of the jokes.
“The Thirteenth Floor”. Good flick, lost in the Matrix hubbub.
*Quatermass and the Pit *(US title: Five Million Years to Earth) is a film I’m very fond of, with some interesting SF concepts. Bit British, though.
I finally got around to seeing this quite recently, just out of curiosity over the parallels to Alien. Found it pretty lame, actually. The DVD included a second feature, The Monster That Challenged the World, that I found a lot more enjoyable–it displayed a bit of wit and had a better creature. And Hans Conreid as the scientist!
listed by me in post #5 above, along with the first two Quatermass films. You ignore the later ones. But, if you can, watch the original BBC serials the movies are based on. They’re much longer, and the plots are actually somewhat different.
There are a lot of films people have listed that I wouldn’t put as “must-see”, personally. Of course, my own list is different. Here’s an updated attempt at it:
2001: A Space Odyssey
Forbidden Planet
These two are my top-of-the-list SF films, and definite must-sees.
Metropolis – the fully restored version, of course, with original score
Things to Come
The Lost World – the restored version, again. NOT the Eastman House version, despite what some purists say
King Kong – arguably fantasy, but definitely iconic. The 1933 version, of course. I’ll add the 2005 version, too, but ignore the 1976 monstrosity
The Day the Earth Stood Still – One of the best. The 1951 classic still holds up. Ignore the later remake at all costs.
The Beast from 20,000 Fathoms – the ORIGINAL 1950s “monster movie”. It wasn’t a cliché then, because they did it first. And it was also Harryhausen’s first use of his Dynamation/Dynarama/“Reality Sandwich” technique, which was a cost-cutting measure because he couldn’t afford the army of technicians Willis O’Brien had for his movies.
Also, for various reasons, the 1950s monster flicks Them! and Kronos
The Thing (from Another World) – the original, of course., It strayed from Campbell’s story, but it has a lot going for it, despite a few missteps. I also think John Carpenter’s 1982 remake is essential – it’s Campbell played mostly straight, and shows the power the original idea had.
** The Quatermass Xperiment (The Creeping Unknown)
Quatermass 2 {Enemy from Space)
Quatermass and the Pit (Twenty Milliion Years to Earth)** – the essential Quatermass trilogy
Twenty Thousand Leagues Under the Sea – the 1954 Disney version. Its special effects were great, for the period. It’s closer to Verne’s vision that just about any other movie, although they screwed with the plot and threw in Nemo discovering Nuclear Power. It’s also the grand-daddy of the Steampunk movement – Harper Goff’s Victorian design for the sub doesn’t match Verne’s technically correct design, but it is visually extremely interesting, despite its inefficiency – just like a lot of steampunk.
** Journey to the Center of the Earth** – another pretty decent Verne adaptation, despite the addition of a villain, a female character, and a singer. But it starred James Mason, as 20,000 Leagues did. They should have made more Verne adaptations with Mason in them.
It! The Terror from Beyond Space – stupid title, but a great low-budget movie. It’s impossible to believe that “Alien” wasn’t deliberately ripped off from this.
Robinson Crusoe on Mars – Even when it was made they must’ve known of many of its inaccuracies, but this feels better than most SF films of its day. Crashed astronaut tries to survive on Mars. The film Enemy Mine and Andy Weir took notes, I hope.
Star Wars
The Empire Strikes Back
Return of the Jedi – How can you not include the first three star wars filmsd? They gave us a lot of the SF scenes we’d hoped for, but the studios wouldn’t give us – lots of friendly and weird-looking aliens, the spaceport bar, space battles. Who cares if it was more children’s story/science fantasy?
Star Trek II
Star Trek III
Star Trek IV – I’ll take these, despoiute their TV roots and some hokiness.
Bladerunner – talk about iconic. If 20,000 Leagues gave us the start of steampunk, this film jump-started cyberpunk. Stylkish and impressive, with a lot of thought going into the background. If only the story were better.
The Terminator – ground-breaking in its own way, and one of the best SF movies in years. It’s still better than any of its sequels, although I’ll include Terminator 2 on the list, for lots of reasons.
Aliens – a much more satisfying film that Alien, which I have issues with.
2010 – a neglected film, eclipsed by its illustrious predecessor. If they simply took out all of Roy Scheider’s voice-overs, it would be almost perfect.
Robocop – I was unimpressed with this when I saw the previews, but the film is a dark-humor gem.
The Matrix and, to a lesser extent, its sequels
The 13th Floor – excellent adaptation of Daniel Inouye’s pioneering VR novel Simulacron 3
Cloud Atlas
Oh, yeah – I almost forgot. It’s been abused, and it’s really fantasy, but it’s a great adaptation of a massively influential series – John Carter
Other mentions:
The Fly – both the 1957 original and the CRonenberg 1986 re-imagining. Ignore all sequels of both films. They’re both iconic.
Destination: Moon – the fact that Heinlein wrote the script alone makes this of interest, although that doesn’t guarantee anything. Slow by today’s standards, and sometimes embarrassing. But it’s important. Heck, it has Chesley Bonestell art.
Invaders from Mars – I’m a lot less impressed with this film nowadays, but it’s on lots of lists.
The Andromeda Strain – Not many examples from the late sixties/early seventies. Crichton’s novel was a major thing when it was first released.
Planet of the Apes – the original 1968 film. There’s a lot of silliness in it that bothered me even as a kid, but it’s undoubtedly been powerful and influential.
Invasion of the Body Snatchers – a major influence on a lot of people. It’s a scary story, well-told. The inconsistencies bother me, and I think Heinlein did it better in The Puppet Masters (which has been filmed twice, but not really well, and with inconsistencies not in the book). Heinlein’s book predates the Jack Finney novel that IotBS was based on, and Heinlein apologized to his agent for using such a hackneyed idea. But the film hit at the right time – after the HUAC and McCarthy Communist hunts.
Dune – both the David Lynch version (and the tinkered-with “Allen Smithee” version) and the SciFi channel version. Both are ambitious and pretty decent attempts to translate Herbert’s epic novel into interesting visuals, and to depict something far from the comfortable SF environment that playted to the crowds. This is pretty far from Star Trek or Star Wars, and closer to the boundary-breaking properties of literary SF.
I had compiled a list of “must-see” movies in another thread, but 1). they weren’t all sci-fi, and 2). I deliberately left off everything that I had seen on any of the lists other posters had made upthread.
Great minds must think alike. My list got noticeably smaller when I pulled out all the duplicates and non-sci-fi movies. Still, there are some that I’m astounded are not already in this thread. Even if I consider the OP being 15 years ago, that doesn’t excuse the absence of the Back to the Future trilogy!
[ul]
[li]Pacific Rim[/li][li]Avatar[/li][li]Prometheus (despite all its flaws)[/li][li]Oblivion (2013 film with Tom Cruise and Morgan Freeman)[/li][li]Starship Troopers (again, despite all its flaws)[/li][li]Back to the Future (all three movies required viewing)[/li][li]Flash Gordon (1980 version with Sam J. Jones as Flash and soundtrack by Queen)[/li][li]Highlander (soundtrack also by Queen; avoid the sequels)[/li][li]Minority Report[/li][li]Jurassic Park[/li][li]Predator and Predator 2[/li][li]Escape from New York[/li][li]Wizards (1977 Ralphi Bakshi film)[/li][/ul]
Wow - a lotta great sf movies mentioned here!
My personal Top Ten:
Star Wars: A New Hope
Limitless
Dark City
Galaxy Quest
Star Trek: First Contact
Close Encounters of the Third Kind
Aliens
Blade Runner
The Martian
Buckaroo Banzai
Very good, but not Top Ten for me:
2001: A Space Odyssey
Star Trek II: The Wrath of Khan
Star Trek III: The Search for Spock
Star Wars: The Empire Strikes Back
Star Wars: The Force Awakens
Cloud Atlas
The Matrix
Terminator 2
Men in Black
Inception
Interstellar
Looper
Children of Men
There are also some superhero movies (The Incredibles and Iron Man, among others) that are sorta kinda sf, but not quite. They’re… superhero movies.