There are a few movies I'll watch through purely on the recommendations of other people. In many cases, though, I use the half hour test, turning the movie off if the first half hour isn't interesting. In some cases, I assume, this is my loss because the rest of the movie is better and makes the first bit more interesting as part of the whole, but that's a risk I'm willing to take.
There's often a trigger that makes me quit a movie or TV show, like a long conversation full of angsty staring or a story decision that breaks the fantasy the movie is trying to sell. In many cases, it's cringe that makes me leave; watching embarrassing situations is the opposite of entertaining for me, so unless there's a good reason to keep watching, I switch to something else.
I can't think of many examples of movies I've stopped watching, mostly because I didn't like them much. This blog post, however, was triggered by the film Drive after one too many ten second silences in conversation. My motto is "I'm not a connoisseur."