The Notebook (!)
Ghost
Titanic
Time Travelers Wife
Seabiscuit
Runaway Bride
Pretty Woman
City of Angels
Fly Away Home
Ol Yeller
The Pianist
Schindler's List
DH and I did both cry after a book, 'A Big Little Life' by Dean Koontz (about his golden retriever, Trixie). Didn't help that we read it shortly after we lost our own dog.
I just remembered, Toy Story 3 made me cry. Darn the last 5 minutes of that film!
I don't watch most animal movies, because they are always sad. . . the animal always dies in the end. That's what makes me sob and snot up. Oh gosh, and the scene in Dumbo when his mom is in the train and rocks him in her trunk? Makes me a complete mess. Even typing about it right now chokes me up.
As far as Where The Red Fern Grows, no. Just. . . no. The book is on my 8 year old's bookshelf, waiting for whenever she would like to read it. When I bought the book and brought it home, I showed it to her and said, "This is a book that I absolutely will not and cannot read to you, not now, not ever." I couldn't tell her why because it made me cry even saying that much about it to her.