What?!? No one has yet mentioned the all-time weepie…
The Champ, starring Jon Voight and Rick

Schroeder. (How anyone can get through the closing scene without bawling is beyond me.)
I had a teacher who once said, “I cry at supermarket openings.” That saying fits me so well. So I love movies that give me a good cry:
Wizard of Oz (don’t know why but the final scene…)
It’s a Wonderful Life (the ending, not so much the scenes involving Mr. Gower, as it did for a previous poster).
The Princess Bride (the final “As You Wish” at the very end.)
Going My Way (the scene in which Mother Fitzgibbon comes in was the only scene that could bring tears out of my he-man father)
Les Miz (the death of Jean Valjean “Am I forgiven now?”)
Father of the Bride (the Steve Martin version. My husband will be soooo like him if God wills our daughter gets married years from now)
Gigi (the proposal scene)
I Remember Mama (when Mama sneaks into the hospital to see her little daughter)
Rogers and Hammerstein’s Cinderella (the Lesley-Anne Warren version), Stuart Damon’s portrayal as the prince was very moving.
Carousel, the final meeting between Billy and Julie
Monsters Inc (when Sully says goodbye to Boo)
(Dang! This list is making me think whole neighborhoods of Costcos are opening! ;D)
Now, some supposed tearjerkers that just don’t do it for me:
Love Is a Many Splendored Thing (really stilted dialog in some places)
Steel Magnolias (Sally Field’s scene in the cemetery was moving but it was spoiled, IMHO, by the ganging up on Shirley Maclaine. It felt like the powers-that-be didn’t know how to end the scene and put it in for a laugh).
An Affair to Remember (and I love Cary Grant)
Someone upthread mentioned Somewhere in Time. I’m from Michigan and love Mackinac Island, where it was filmed. Pretty as the movie is, the movie was just so-so to me: He didn’t go back in time (he hypnotized himself) and Christopher Reeve was just so wooden.
And finally,
The Sound of Music. This should make me cry, but it just doesn’t move me. At all. Don’t know why. Perhaps part of it is that it veers so far from the actual story but it didn’t move me when I first saw it either, before I knew the whole story.