I agree. Most girls like a good romance story and it'll make you look good, show your sensitive side.
Also if you want her to hold onto you it is also a good idea... Though it might involve you making the first move. During a teary part I'd suggest either putting your arm around her or holding her hand...
Of course this is all very cliché.. but I think it would be more effective than a horror flick which might give her the wrong impression.