I saw
The Matrix,
American Beauty,
Fight Club, and
The Talented Mr. Ripley without knowing anything about them. I'm glad I did, because I think I enjoyed those movies even more because of it. More recently, it's hard for me to say... I don't go to a ton of movies. Oh, I didn't really know anything about
Watchmen when I saw it in the theatre. Maybe that's why I enjoyed that one too
It's no coincidence that the first four movies I mentioned all came out when I was in high school, and when the internet was less mature. The information about the movies wasn't as easily accessible, I didn't have the time (or autonomy - I didn't have my own computer) to find out more about movies, and my friends and I would just go to whatever movie seemed like it might be good, even if we didn't know much about it. Now, I'm more picky about what I see in the theatre, and it's a lot easier for me to learn about a movie beforehand (both intentionally and unintentionally).
I definitely think it makes a difference when you truly have no idea what's next. On one hand, I'd love to see more movies without knowing anything in advance, but on the other hand it's difficult to make that kind of time and money commitment these days if I'm not pretty sure it's worthwhile.