Often. More than often - I cry a lot, usually. But on the other hand, I'm laugh a lot, so it balances out, in the end.
Last two movie that got me crying for hours, even after they were over, were Québec's
Polytechnique, about a shooting in the uni I frequent, and
Dédé - Through the Mist (sheesh, just the preview on that last linky got me teary), about a signer that commited suicide (by hara-kiri!) 10 years ago.
Also in the list The Passion of The Christ, that left me in a state of physical shock (I was sick for a week after seeing it - I can't stand seeing pain), La Vita è Bella, Little Women (I was young!), LOTR The Two Towers (I just don't know why though, but the first time I saw it I cried all along, from start to finish), LOTR The Return of the King (because it was the end) and a few others that I can't remember now...
The key, to save face at the end of a sad movie, is to run to the bathroom to complete the crying session in peace. I have vivid memories of my mom and I rushing out of the living room to blow our noses and regain composure after every sad movies we watched...
As for books, the most memorable tear jerkers for me are Ester Mazel, by Frédérique Hébrard, Rilla of Ingleside (Walter!) and the two last Harry Potter (maybe because I got to the dramatic part of both books around 7 in the morning after pulling all nighters because I couldn't put the books down). I know that book wise, there is more, but the ones I just listed I remember needing to put down often because I just could not read anymore.