I've never actually been to a movie theatre alone, but when I lived in Ottawa while in University, I went to a bunch of museums by myself, and it was seriously the best thing I ever did.
Some of them had Imax theatres in them, and I would watch films in there alone also, and it really wasn't that bad at all. It took me a while to build up the nerve to go by myself, but once I was actually there I found myself more caught up in the exhibits or the films, and not so much on what other people were doing or thinking.
EDIT: If you're planning on going to a museum by yourself, try not to set of an alarm!!! This can cause extreme awkwardness and embarrassment! (haha, worst moment of my life)