Yes. It does happen. Although it’s more common for people to leave a theater because they find a movie offensive than boring.
Oddly, most people will sit all the way through a movie that they find boring, and they always say afterwards, “I kept hoping it would get better.” Don’t do that to yourself. If a movie is boring in the first 30 minutes, I can pretty much guarantee you it’s going to be boring for the next hour and a half.
Anyway, most theaters will happily refund your money or exchange your tickets for a different movie if you come out within 30 to 40 minutes after the feature starts and let them know you’re not enjoying the show. Most people who work in theaters are also movie lovers, so they understand and honestly want you to see a movie you find enjoyable.
However, if you stay and watch the entire feature and then ask for your money back, you are unlikely to get it.
Unless you make a huge fuss, in which case they may give you passes to get you to go away, but let’s face it – being given passes by someone who just wants you to go away is like regressing to toddler age and having a temper tantrum to convince your parents to buy you a candy bar at the supermarket. Except more inappropriate. Because you’re an adult. And the movie theater manager can’t put you in time out.
Essentially you are paying the theater to project the movie you’ve selected onto a large screen. So if the movie was projected onto a large screen and you watched it, you got what you paid for.
The theater has absolutely no control over the quality of the films that it shows, and your ticket doesn’t guarantee enjoyment – it guarantees only that you’ll get to sit in a dark room and watch the movie with a crowd of strangers (or, if you’re going to that obscure, low-budget, indie film in the smallest auditorium, possibly with a crowd of one stranger).
Asking for your money back after the film is over is like buying a loaf of bread at the store, eating the whole thing, and then returning the bag to the store and asking for a refund because you didn’t like it.
But the answer to your question is: Yes and usually (assuming they come out within the first 30 to 40 minutes after the feature starts).