I totally get it - while that isn’t something that pushes my own buttons, the two movies I named in my OP (American Beauty and The Nineth Configuration) make me cry because they do hit particular notes that speak to me in intimate terms, based on my own experiences and values.
It’s when a movie touches on something deeply personal, for whatever reason, that the waterworks start to flow. That could happen in a lot of movies, not just ones designed to pull at heartstrings.
In 2021, I had my girlfriend over for dinner, after which we screened Yesterday (she was a huge Beatles fan). I had seen it a couple of months earlier, but it was new to her. Much to my surprise, when the protagonist visited the house out in the boonies and the door opened to reveal John Lennon, I just dissolved. I had to pause the movie and cry in her lap for a bit.
Then, of course there’s The Dirty Dozen (clip contains spoilers for both movies).
Seriously, an obscure movie to see, once (that’s my limit) is My Life Without Me. A young mother (Sarah Polley) finds out she only has a couple of months to live and creates a bucket list. Hilarity does not ensue.
One was ET. Nor when he dies, but when the kids show him to their mother. She is frightened and takes them away, and he reaches out his hand and cries. He’s sick and dying a long way from home and now he’s being abandoned.
The other was Barry Lyndon. A young boy has been mortally injured in a riding accident. As he lays in bed dying his estranged parents are at his side, one on one side and one on the other. He asks them to stop fighting with each other. The scene abruptly changes to his funeral procession, and his coffin is borne on a small cart drawn by goats, a vehicle he use to play with; The time I saw that with my then husband I turned and started bawling on his shoulder.
An old one, but “West Side Story”. That speech Maria gives at the end — “How many bullets are left?” — always leaves me sobbing, no matter how many times I’ve seen it.