By default, I watch movies like most anyone else does -- get immersed in the story, subconsciously appreciate the component aspects like cinematography, editing, sound design, etc. If any part of the movie is particularly bad (writing, acting, camera work, any aspect of the soundtrack), causing me to fall out of the story and back into the theater seat (or couch), there's a chance that I'll start scrutinizing the components that make up the film, including sound. If the film is excellent all around, I may consciously appreciate some component of it for a moment or two before getting back into the story.
On good films like those, if the element that grabbed my attention is a great sound moment, I always watch the film again later to do nothing but scrutinize the sound. I did this most recently with Avatar to the tune of yet another $18 3D IMAX ticket -- ouch. (Chuck, yes, the sound was good - I loved the mix and there was plenty of killer FX work.)
If the movie is just horrendously awful, I'll try to make the best of it by turning it into a listening exercise and scrutinize every last iota of sound work that I can.
I find it harder to stay in "story mode" when gaming - possibly because I have to listen critically while gaming day in, day out at work. Habit, I guess.