This may well be the cheesiest thing I've ever written, but the scene in Grosse Point Blank where John Cusack is holding the baby and ... well, they have a moment. That was some brilliant cinema right there. I cry, but in a sort of happy-sad way, if that makes any sense.
The scene in Deep Impact where Leelee Sobieski (sp?) has to say goodbye to her parents and they hand her the baby kills me every time, too. I can watch it, rewind it, watch it again, rewind it and watch it a third time and I'll have fresh tears with each viewing.