A possible kidnapper could be a rogue demigod from his own camp. Someone who has been corrupted by power or jealousy. They might see Percy as a threat to their own rise within the camp. Also, it could be a follower of an old Titan or Giant. Just because the main battles were won, doesn't mean there aren't still remnants of those forces out there, and they might think Percy is the key to bringing back their former masters.
It could be a vengeful minor god. Maybe a god who feels that Percy or the demigods in general have disrespected the gods too much. This god might think that by kidnapping Percy, they can teach the demigods a lesson. Another option is a powerful monster that has a grudge against Percy specifically, like a particularly smart and devious Cyclops who has been plotting revenge.
It could be Luke Castellan. He has a history of being against Percy and the Olympians. He might kidnap Percy to gain an advantage in his own quest for power. He could use Percy as a bargaining chip with the Titans or other powerful forces.
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.