I just remembered two more! Other than the Last of the Mohicans of course, because I thought that was the nicest "love" story ever (despite the tragic events of war) when I was a youngster of 12 and Daniel Day Lewis was so hot (MUCH better than he was in the Unbearable Lightness of Being ).
I used to LOVE Beetlejuice, and most unusually, when I saw it again only recently, I really began to wonder why I used to like it. The cartoon was wonderful though, and remains that way.
Also, of all sappy things to like, I loved Fried Green Tomatoes.
Others that I can remember are
Sleepless in Seattle
Austin Powers (the first one ONLY)
Sliding Doors (one of my absolute favorites)