Hard to believe that no one’s mentioned Godfather II yet.
Deerhunter could qualify. Small town Pennsylvania life followed by Vietnam horrors. It’s been a while since I’ve seen it though, I may be forgetting some things.
Cemetery Man (Dellamorte, Dellamore) has got to be in this list, though it is most apparent when watching the original version and not the chopped up versions that played in the US. The first 2/3 of the movie is a pretty straightforward zombies-arise-from-the-cemetery movie. After that point, it becomes sort of a surrealistic morality play. The ending is wonderful and mystifying (to some) way to end a fairy tale.
(Other posters are welcome to comment on the DD background of the movie, but it’s not relevant to the two-movies-in-one aspects, IMHO.)
Event Horizon and Sunshine were both engaging, semi-intelligent sciency fiction movies that became terrible horror movies.
The inside of your head must be a interesting and terrifying place. 
Three movies if you count the wedding.
Four Weddings And A Funeral - five movies!
I thought 500 Days of Summer would never end.
Cloud Atlas—six in one!
Prospero’s Books was two different movies running simultaneously. One was Shakespeare’s The Tempest, the other was a lot of naked people all over the place alternating with some extremely cool book art.
And yet, The Neverending Story did. 
Not only that, it had a sequel. How can a Never-Ending Story have a sequel? Isn’t that like “To Infinity … and Beyond!” ?
21 Jump Street was a silly comedy until it suddenly became an ultra-violent action cop film. The turning point came when one of the bikers fell under a semi and was quite graphically crushed to death.
How can a never-ending story not have a sequel?
I really enjoyed that Jack Nicholson movie about the world of publishing, with what felt like some well written insider dialogue, great cast and awesome shots of the Bradbury Building.
Too bad they mixed in a bunch of tiresome werewolf stuff.
Four Rooms is essentially four mini movies.
It does for me. I haven’t seen all the films mentioned upthread, but I’d say Mulholland Drive is the best example of two films in one. Many plots will take a story into new surroundings (e.g.: starts with action, ends up in courtroom) and the vast majority of them will show a transformation of the story itself and/or of the characters. Mulholland Drive is the only film that I’m aware of right now that juxtaposes the two very different stories that it contains. Actually, metaphorically speaking, “superimposes” might be a better word, because it’s not just that the beginning and end are noticeably different, but rather that, if you want to understand the story, you have to use the clues in one part to draw conclusions about the weirdness in the other part. There’s no linear development to be considered in reverse by your mind’s eye (walk back through the story), but rather, you have to simultaneously consider two opposing realities, not unlike the ordeal of Naomi Watts’ character.
Because it’s like asking “What comes after infinity?”
It’s its own sequel. At the end you hit play. Lather, rinse, repeat.
Didn’t say it was going to be a different sequel.
Predator. The first part is about a CIA mission, the second part is vs. the Predator.
But really, and the mention of Return of the Jedi reinforced this, it’s actually a very very common trope in stories (not just movies, but novels too) to start with some sort of situation and explore that situation a little before transitioning into the real story. Often the setup story is about one job of a team before they start gearing up for the main job. Think of Inception or Mission Impossible (all of them, I assume; I haven’t seen most). A lot of the movies mentioned here fall into that pattern, including the one I mentioned, which only triggered in my memory because the guys hosting it on cable (back when I had cable, wow, that was a long time ago) explicitly said it was two distinct movies as part of their banter. As noted, I somewhat disagree with that; the first act of the movie is necessary to meaningfully set up the rest of the movie. You need some reason for Arnold to be in the jungle without any sort of support; the bulk of the movie simply could not exist without the “filler” that sets it up.
The old John Wayne movie The High and The Mighty is pretty much two separate stories - the flight crew’s and the passengers’ - with Wayne being the crossover character. As a matter of fact, I don’t think Robert Stack’s character even appeared in the same scene with any passenger.
Seconded. Godfather II is such a perfect double movie that they could cut it in two, stick the first movie in the middle, call the whole thing The Godfather Saga and still get a coherent story out of it.
Yes, it’s true of novels too. Which is why I typically start reading a novel somewhere in the middle. To skip that unnecessary “other” novel they’ve bulked out the pages with.
From my point of view, a lot of movies used to end with a long meaningless fight/dance/chase. Pretty much unrelated to the story. In modern blockbuster movies, they’ve “fixed” that: pretty much the whole move is a long meaningless fight scene, dropping most of the “filler that sets it up” 