I've seen 33. The ones I have not seen are Pride & Prejudice, Slumdog Millionaire, Dear John, Love Story, and Before Midnight (never even heard of that one).
ETA: I have seen Carol, I originally thought I hadn't because it's such a generic movie title, so I didn't realize it was one that I have actually seen.
I watch Bridget Jones Diary often. Brokeback Mountain I've only seen once because my entire face was swollen from crying and although I love the movie I don't want to go through that again. An Affair to Remember, ah, so good.
I was thinking "I don't watch romance movies", but then I went through the list and I've seen 17! I guess I need to rephrase that to, "I don't like most romance movies." I did like While you were Sleeping though.