The animations that play on the onset of each route.
The game being able to pull off such delicate subjects without being insensitive at all.
Emi, despite losing her legs in a tragic car accident which claimed the life of her father, continued running using prosthetics, and is the best runner at the school, at that.
Also in Emi's route, who comes to the rescue when Hisao and Emi almost break up? It's someone whom you wouldn't expect... Misha! Shizune also deserves some credit for telling Misha to intervene. Quite the surprise, and if you take her advice, she'll be the key to getting back on the path to Emi's Good Ending.
Deconstructed in Hisao throwing away Iwanako's letter, without even reading all of it. At first it seems like an awesome moment by itself, demonstrating Hisao's Character Development, but when you consider what the letter meant to Iwanako, and that the letter is a result of a Break the Cutie process for her, then it gets turned on its head. It's nice to see Hisao look forward to the future, but not necessarily when he unintentionally ends up hurting someone, especially a girl as painfully shy and fragile as Iwanako. Also, Hisao's act is meant to mirror Emi's tendency of running away from the more painful elements of her past by pretending they aren't there and always blazing full-speed ahead.
The real Crowning Moment of Awesome is when he retrieves the letter and reads completely, putting his biterness behind him.
The tour Hisao gives Misha of the school late in Shizune's route, recalling all the experiences he's had with her and Shizune, and urging her not to push Shizune away like he did with his old friends. It showcases his Character Development and is a crucial step in repairing Misha and Shizune's friendship
The fact that Hisao is Above the Influence and manages to keep his desires in check when Hanako (whom he has an established crush on) comes on to him whilst drunk after her birthday party.
When Hanako has a panic attack in class, Mutou and Shizune know exactly what to do and how to help her.
By her Good Ending, Hanako has managed to successfully open up by herself.
Even in her Bad Ending, as painful as it may be, she has the courage to tell Hisao that his pity makes her uncomfortable.
Hisao's Race for Your Love scene in Lilly's Good Ending. As heartwrenching as it is that Hisao has a heart attack mere meters away from her at the airport, the fact that he travelled so far just to say goodbye to her one last time is awesome in its own right. And what's more, it actually worked, convincing Lilly to stay with Hisao in Japan and giving the couple the happy ending they deserve.
By the end of Lilly's route, Hisao himself has managed to survive and recover from not one, but two major heart attacks. The man is nothing short of determined, to say the least.
Hanako gets one late in the route: she decides to join Naomi and Natsumi's newspaper group, and plans to travel to Kyoto with them. And she does this all on her own.
Similar to the moment in Hanako's route, Hisao is Above the Influence when Rin kisses him while high on cough medicine (which she took far more then the prescribed amount of).
Not so much to do with anything within the game, but it has been mentioned that this is the first Visual Novel to end up on the front page of Game Faqs, placing 1st on the most wanted Faqs on the site before someone submitted a complete Faq. At its peak, it made the 3rd top rated PC game and 11th top rated game.
Within two weeks, the Katawa Shoujo thread has become the second largest thread on the Visual Novel section of the forum.