In my fanfiction, during a Quidditch practice, Ginny Weasley has an accident. She's flying really high, trying out a new maneuver. But a strong gust of wind blows her off course. She collides with one of the goalposts. Her teammates rush to her side. Luckily, she only has a few bruises. However, it makes her more determined. She spends the next few days training extra hard to improve her skills and avoid such accidents in the future. She becomes an even better player after this incident.
If a player had a serious Quidditch accident, like breaking a leg, the immediate aftermath would be chaos on the pitch. Teammates would rush to their side, and the game would be stopped. The injured player would be taken to the hospital wing. In the days that follow, their team would have to adjust their strategy without them. The player would be in a lot of pain and have to go through a long recovery process. Their friends would visit often, bringing them notes from class and treats from the kitchen.
There's a fanfiction called 'Accident at the Ministry'. In this one, Harry accidentally activates a powerful and ancient magic while at the Ministry of Magic. It sets off a chain of events that involve him having to team up with some unlikely allies to fix the mess he's made. The story has great character development and a lot of action.
One possible scenario could be that a group of Hogwarts students, while exploring a hidden cave near the Forbidden Forest, accidentally trigger a magical trap. Maybe they were searching for some rare magical ingredient for a potion. The trap could be a spell that causes the cave to start collapsing, like the rocks begin to fall and the entrance gets blocked. They then have to use their magic skills, like levitating the rocks or using the reducto spell to clear a path out.
Characters could survive a cave accident in a Harry Potter fanfiction by relying on their knowledge of magical plants. Maybe there are some Devil's Snare plants in the cave. If they know how to handle them, they can use the plants to their advantage. For example, they can make a rope out of the Devil's Snare to climb out of a deep hole. Also, they can use their wits and the skills they've learned in their classes. If it's a cave filled with dark magic, they can use their Occlumency skills to protect their minds and then find a way to counter the dark magic using spells like Lumos to find hidden passages or exits.
One interesting 'Harry Potter accident' fanfiction could be about a spell gone wrong during a Quidditch match. For example, a bludger might accidentally be enchanted to multiply, causing chaos on the pitch. Another could involve an accident in Potions class where a wrong ingredient makes the potion explode and create some unexpected magical effects. There might also be a fanfiction where Harry accidentally travels back in time due to a malfunctioning Time - Turner.
Neville could be a great main character for this kind of fanfiction. He's not as confident in potions as some others. So, an accident where he creates a potion that makes all the plants in the Hogwarts greenhouses go wild and start to overgrow and take over parts of the castle would be an interesting story. He would then have to use his knowledge of Herbology to try and control the situation.
Often, Harry Potter himself could be one of the main characters in such fanfictions. Maybe he has an accidental love encounter with a new character introduced in the fanfiction, someone who might be from a different house or have a unique magical ability.
Perhaps in the fanfiction, Harry is under the influence of a dark spell that causes him to hallucinate a car accident. This trauma could be so severe that he starts self - medicating with a dangerous magical substance, becoming addicted. Or maybe he's on a mission in the Muggle world, gets into a car accident, and while in the hospital, he's given some strong painkillers that he then becomes addicted to. But it's important to note that this is all very much against the normal Harry Potter narrative and more of a creative and often disturbing exploration.