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Tear Jerker: Outlaw Star
The episode "Cats and Girls and Spaceships" from Outlaw Star, where Jim unknowingly kills the girl he had liked, and when she understandably fails to show up for their date afterward, he assumes she stood him up and never finds out the truth.
God, I bout bawled my eyes raw. It's not just that he dies. It's the way he says goodbye to Melfina.
Suffice to say, if their name starts with an H, you're going to cry when they die.
The very, very end of the series, with the the whole crew reunited and setting off for new adventures, always makes this troper teary eyed, both because it's such a good send off and embodies the spirit of Outlaw Star, and because we won't get to see those adventures. The ending caption seals it.