AI, Artificial Intelligence, and The Green Mile. Those are the only two movies made this decade that have brought tears.
For the 90’s: Shindlers List.
Another vote for Grave of the Fireflies. Not only did it bring tears to my eyes on several occasions but at one point near the end (the montage with Home Sweet Home in the background) I nearly sobbed openly.
I suspect that there are very few people who could watch that film without coming at least close to tears.