I also noticed that they omitted "I Love You Philip Morris", one of his legitimate (i.e. non-comedic) crying movies . (Though he is overshadowed by the brilliant waterworks of Ewan McGregor.)
"Eternal Sunshine" is a nice one too.
Climbing to a high chamber in a well of houses, he threw himself down in his clothes on a neglected bed, and its pillow was wet with wasted tears. -- A Tale of Two Cities