I'm not all that sure to bring them up, but ever since I was 9 years old I've loved creepypastas, I read my fair share of horrifying (in more ways than one) stories, of course. Back in the day Zerodragon243 had my favorites, he wrote and edited his own pokemon-based stories, dark passages that referenced many of the established but usually ignored elements from a horror perspective.
"Icy Song" takes up one of Froslass's pokedex entries: "Legends in snowy regions say that a woman who was lost on an icy mountain was reborn as Froslass". It is about a young singer who lost her voice and consumed by despair, in her desire to recover it, she goes into a blizzard and arrives in a temple of frozen lands, she made a pact with a spectral voice, but in reality it's just a hallucination, she died from the cold and became a froslass. The title is also a reference to the spanish name of an ice-type move, "Ice Shard" adapted as "Canto Helado".
"Our World" gives a pessimistic perspective on the pokemon world and how the structure given in the games, as humans and pokemons by that eagerness to battle and force themselves to go beyond their limits sets them on a painful path that most of the time ends badly, and despite that, no one seems to care. A world where pain is a game and blood our currency; as players we are motivated to hurt our characters again and again for experience and extra money. It is a curious vision as it makes us question something we take for granted, in this case, violence... Something that curiously PokeSpe manga dealt with superficially in B&W saga.
There are many stories based on pokedex entries such as "Explorers," a story told in the form of a research log about a Flygon that migrated from Hoenn to Unova. Some narrate in-game events such as the clash between Kyogre and Groudom from a civilian perspective, those powerless to make a difference, those powerless in the face of tragedy. And "master" is... certainly a heartbreaking story of brotherly love between trainer and pokemon, a tourch-passing story about safeguarding the future of those yet to come and how our memory can live on in others. All these stories are quite old, more than 10 years old, and the author has long since passed away. "Master" was his final work, a way of saying goodbye before the disease took him away. He shared his passion to the end and encouraged everyone to make their own stories, I still revisit his work every time I want to go back to that time.
I also really like stories about hackroms that tell their own story or what if scenarios, it's a curious form of story telling like Unown King or Strangled Red. I love even more the ones told in the form of urban legends, but I don't know how much those last ones would fit in the "fanfiction" area.