Maybe Doctor Octopus. He has always been obsessed with power and knowledge. He might kidnap Peter to figure out the secret behind his spider - powers. He could think that by studying Peter, he can enhance his own mechanical arms or gain some new form of power that would make him the most feared villain in the city.
Another possibility is a new villain created specifically for the fanfiction. This villain could be a powerful business tycoon who is secretly funding criminal activities. He kidnaps Peter because he sees him as a threat to his underground operations. He wants to either eliminate Peter or turn him to his side to use his powers for illegal gain.
Maybe it's an old enemy of Peter's who has found out about his friendship with Flash. For example, someone from Oscorp who wants to take revenge on Peter for foiling their evil plans in the past and figures kidnapping Flash will draw Peter out.
It could be an old enemy of Keith's, someone from his past who has a vendetta against him. Maybe a former rival from his days in the military academy who has now turned to more devious means.
In some creative fanfiction, it could be an alternate version of Spiderman himself from a different dimension. This Spiderman has gone bad and kidnaps a fan from our dimension as part of some grand, dark plan that involves crossing dimensions and causing chaos.
A power - hungry nobleman from a neighboring land could be the kidnapper. He might believe that by having Rapunzel in his possession, he can gain some sort of political advantage or use her as a bargaining chip against her kingdom.
It could be Orochimaru. He's always been interested in obtaining powerful individuals for his experiments, and Naruko with her unique abilities would be a prime target.
It could be a new villain that has emerged, someone who is jealous of Gohan's power and wants to make it his own. This villain might be from a far - off planet and has heard of the Saiyan legend.
It could be a group of rogue Decepticons who are acting on their own. They might not follow Megatron's orders but still see value in kidnapping Arcee. Maybe they have a personal vendetta against her or think they can get rich by selling her to the highest bidder in the Cybertronian underworld.
Maybe it's a group of villains working together. They could be from different factions but united by the idea that Izuku has the potential to become a huge threat to their plans. They might kidnap him to either eliminate him or turn him to their side. Also, it could be a lone, obsessed fan of a villain who wants to prove themselves by bringing Izuku to their idol.
A group of outcasts from different islands might kidnap Moana. They feel that they have been wronged by the 'normal' society that Moana represents. They hope that by kidnapping her, they can get the attention they deserve and force the islands to change their ways. But Moana listens to their grievances and tries to find a way to help them while also finding a way home.
It could be Zeref. Since Zeref has an interest in powerful magic users and Natsu is a strong dragon slayer, Zeref might kidnap Natsu to study his magic or use him in some dark plan related to his quest for immortality or power.