I think Chaplin’s The Kid was huge - it made it standard that comedies could be as long as serious films.
The Seven Samurai*** was a template for tons of American Westerns.
Night of the Living Dead was a gigantic turning point in horror, and invented the zombie (in the brain-seeking flesh eating sense) movie.
I want to say The Thin Man, but I can’t think of why, except it ‘influenced’ twelve more movies pairing William Powell and Myrna Loy.
[Comic Book Guy Nitpick]
The zombies in Night of the Living Dead and its sequels aren’t particularly interested in brains. They just want to eat people. They aren’t picky about which parts.
[/CBGN]
Nosferatu, the granddaddy of all vampire films.
[ShelbyvilleEquivalentOfComicBookGuy]Well, they weren’t called zombies, either. But you knew what I meant.[/SEoCBG]
I’ll see your Jaws and raise you a Star Wars. After Star Wars, Hollywood chased Big Blockbuster more than they did previously. It also was a breakthrough sci fi pic - previously sci fi tended to be a kitchy niche, 2000: A Space Odyssey notwithstanding.
I second Birth of a Nation: before it was made movies were more of a gimmick than a popular art form.
I know it’s not a movie[1], but I’d say Neon Genesis Evangellion was more influential than Akira, because of the sense of possibility it gave Japanese anime creators. Similar to Birth of a Nation, in a way. It also had a lot more direct imitators than Akira.
Yes, but I’ll add that it was also heavily influenced by American Westerns.
Another big influence is… Stanley Kubrick. I once read an article showing individual shots of his movies later being imitated multiple times. http://whatculture.com/film/50-reasons-why-stanley-kubrick-is-the-greatest-director-of-all-time.php
I’d add Rashomon to the list, but some remember that film a little differently. 
[1] Evangelion was a 1990s Japanese TV show that was a proportionately bigger hit than Star Wars. A couple of movies followed. It’s currently being redone as a 4 part animated feature: parts 1-3 have been released. Neon Genesis Evangelion - Wikipedia
It asked more thinking than I was able to apply to it.
Make head or tails of the movie? I’m sorry, Dave, I’m afraid I couldn’t do that.
I had to ask my then-roommate (who had read the book) to 'splain me what the story was.
Animal House (1978) launched the “gross comedy” genre.
My problem with Star Wars is that it killed the science fiction genre and replaced it with sci fi. Star Wars didn’t even invent sci fi - it had been a popular genre back in the fifties. Star Wars just revived it.
There are those who believe that Star Wars’ influence was wholly pernicious, and that the Hollywood blockbuster mentality leads to movies that are crap or one-dimensional at best. Also merchandising. But bad influences are still influences.
That said, 1950s sci fi films were all low budget and mostly shlock, the Day the Earth Stood Still and maybe Forbidden Planet notwithstanding. Rather enjoyable shlock according to my tastes, but still shlock. I mean Day of the Triffids, The Fly and the Invasion of the Body Snatchers are awesome and even possess some semblance of intelligence-- but they’re still shlock.
Godzilla.
Either the original or the Perry Mason version.
We’d never have had Ultraman, Pikachu, My Neighbor Totoro or tentacle porn without it.
I would have said Metropolis; a lot of cinematic science-fiction can trace its origins back to that.
Also, for some directors, Kurosawa’s films.
Here’s a very interesting side note:
I’ll add Destination Moon to that list!
I think a call-out to both Wizards (1977 animated) and Heavy Metal (1981-ish animated) should be mentioned, as for the time of release, both were rather notable in that genre, becoming ‘cult classics’ pretty quickly (mainly multiple theatre-rooms midnight-showings on weekly basis for years).
Certainly not tremendously influential, but it did draw a LOT of movie-goers on a regular basis. In Austin, I had to wait in line early to get tickets as they both were usually sold-out (or nearly so) pretty quick, IME. I also must have seen Rocky Horror Pic Show at least a multiple-dozen times at Riverside Theatre showings (~early 80’s, fwiw) in Austin, squirt-guns/rice and virgin call-outs and all Fun times, but I am not really aware of how much they influenced later productions of similar movies. They both had a big influence on a certain population, though, no doubt at all.
The Good, The Bad, and The Ugly was arguably the movie that started the whole lone wolf, avenging angel leading man genre, and not just for westerns.
How about Deliverance?
Forty years later, you can still find ‘Paddle Faster, I hear Banjo Music’ T-Shirts.
It’s probably true for people in my age bracket (70’s) but I can’t think anything bigger than A Streetcar Named Desire (1951)
Am I missing The Great Dictator (1940) or over-rating it? It did show silent did not equal dead at the box office.
Some of the films mentioned have influenced only the business of movie making. There are movies such as Birth of a Nation, Guess Who’s Coming to Dinner, Deep Throat, among others that had greater breadth of influence.
I think The Grand Illusion deserves honorable mention as it was worshipped by all the Hollywood guys in the '40s (Orson Welles among them).