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Tear Jerker: The Secret Garden
All of The Secret Garden films qualify at some point, with the 1993 version being a particularly heartrending offender.
"You brought us back to life. You did something I thought no one could do."
The entire scene is very sad and moving, after Colin and Archie are reunited, Mary runs off in tears, and says "No one wants me!". She tells Lord Craven she took the garden because it wasn't wanted, Lord Craven comforts her and assures her he won't lock it up.
Depends on how easily moved you are, but several instances bring happy tears, and the '93 movie has a terribly sad dream sequence.
Also in the 1993 film, the moment when Colin and Archie finally reunite, and Colin doesn't even know it at first because he's blindfolded from playing blind man's bluff with Mary and Dickon.
YMMV on the anime series, but it does have several moments that are genuinely sad. Like Mary having an Heroic BSOD after meeting Mr. Craven for the first time and thinking that he hates her, the (surprisingly well-done) ending in which Colin finally can walk again, calling out for his father, the flashbacks to Lillias Craven's death, or the story of the Canon ForeignersCamilla and Max Hawkins.Specially in the case of Camilla, who is one of the biggest Woobies in the series.
In the 1987 film, The Reveal that Dickon died in the war.