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Tear Jerker: Hikaru no Go
When Akira first joins the Kaio Middle School Go Club, three jealous students decide to try and trick him into a 'fair' game, where he has to play against them without ever looking at the board. When the bullying gets discovered, he gets yelled at — "If you weren't here, this wouldn't have happened!" While she quickly retracts this, the Club President later confronts him with news that one of the students quit the team, and quietly asks why he chose to join, implying he'd rather see Akira quit as well.
Sai disappearing. Saddest moment of the series, hands down.
Hikaru's resulting spiral into depression, blaming himself for Sai's disappearance and wishing he'd been less selfish (which is ironic, as it is Hikaru's drive to develop his own skills and not merely serve as Sai's vessel that allows Sai to let go of his quest to play The Divine Move.)