I have to agree with some of you who have already posted, the Princess Bride and the Untouchables are two of my all time favs....
Another from the Untouchables:
http://youtube.com/watch?v=Gf1sV1K0LiI&feature=related
Two of the most romantic scenes of all time:
The agony of Pride:
http://youtube.com/watch?v=L_NA0GFf1O0&feature=related
My favorite scene of all time:
http://youtube.com/watch?v=YFNgcYN5_jw&feature=related
One of the cutest opening scenes....
http://youtube.com/watch?v=hA14VJJ_j8I&feature=related
And one of the cutest endings...
http://youtube.com/watch?v=_Wh6cx4hamU&feature=related
I couldn't find any specific scenes but here is the trailer from Freedom Writers, an amazing movie for anyone but especially those of us who teach!
http://youtube.com/watch?v=lejN7Ulh10s&feature=related
A sad, yet romantic ending paired with one of the best songs ever written:
http://youtube.com/watch?v=in0lmaykmyg&feature=related
Any oldie but still romantic as ever:
http://youtube.com/watch?v=pa-dGYjSq5k