Hey Martin, I do this.
I used to keep my list in a word document, but I recently switched over to Google Documents. I know it's not really a "logging service," but it works well for me. I sort by the director's last name and include the film title, year, and date I watched the film on the same line.
I also keep a list of every book I read, show I go to, and record I buy. That probably seems pretty pathetic, but I just can't help myself! I love indexing and cataloging things.