Yep, I've done it. Like you say, much more difficult these days with the prevalence of the media discussing it and showing too much of it. But I did manage to go into Trek 09 pretty much blind and I had a much better experience because of it. I hadn't even watched the trailer until I was sure I was going to go and see it with a friend which was a few days beforehand. In general, I much prefer not following movies so closely that I know everything beforehand. I think it ruins the element of surprise, but it's frustrating when the publicity is structured as to sometimes ruin those surprises.
But on the other hand, I've come to realize that if they hardly talk about the movie itself, that something sounds wrong. For example, when Harrison Ford was promoting Indy 4 and doing the publicity tour, I remembered watching him on a talk show and while they had spent a lot of time on him, he hadn't talked about Indy 4 or given any details about it other than it was coming out.