This is based on opinion. Please don't list it on a work's trope example list.
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.
The Haze Middle School Go Club losing the first tournament. Not only did Hikaru lose to Akira, but all of the players lost. Everyone except for Yuki start crying. The icing on the cake is when Akira tells Hikaru he once thought that he would be able to play the Divine Move. Since he was playing Hikaru instead of Sai, he was really disappointed in Hikaru's skills.
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.)
Isumi making one tiny mistake during the pro exams. Hikaru notices it and tries to ask Isumi about it. Isumi then forfeits the game and suffers through a huge Heroic B.S.O.D., constantly kicking himself for unintentionally cheating. What's more is that he loses two more games, one of them against Fuku, and fails to make it past the exams again. However, he manages to pummel Ochi who was the one who threw him off by telling him that Akira is after Hikaru.
During the Young Lions Tournament, Sai and Ogata are both observing Hikaru's game. A table opens up next to them, and for that single moment, Sai forgets he's a ghost and invites Ogata to play a game with him. Of course, he doesn't hear him.
During the Pro Exams, after Honda loses, he struggles to get on the bus home. The bus driver takes his cap off, saying the walk might do him some good, and that he can always take the exam again next year. Hearing it said back to him finally makes it real for Honda, and he bursts out in tears.