It could be a jealous rival host club. They might be envious of the kidnapped host club's success and popularity, so they plan to kidnap them to gain an advantage.
Another possibility is a group of people who have a personal vendetta against one of the host club members. Maybe someone from a character's past has a grudge and decides to target the whole club to get to that one person.
The Yiga Clan could be likely kidnappers. They've always been enemies of Link and would love to get their hands on him. They might see kidnapping him as a way to stop him from interfering in their plans. Another possibility is the Gerudo thieves. Although not all Gerudo are bad, there could be a group of them who think Link has something valuable and decide to take him hostage.
Maybe a secret admirer who is too shy to approach her normally. They think that by kidnapping her, they can have some alone time with her and confess their feelings. However, this is a very extreme and wrong way to go about it. Another possibility is a group of thieves who think Haruhi comes from a wealthy family and they can get a big ransom for her.
Enemies from her past, such as old villains she's fought against, would be likely kidnappers. They might hold a grudge for her previous defeats and want to use her for revenge or some dark purpose.
There could also be a group of villains working together to kidnap Sonic. For instance, a combination of Eggman and some of his more powerful robot creations along with a couple of other villains from Sonic's rogues gallery. They might have a grand plan that requires Sonic's capture, like using his power to open a portal to a world full of chaos energy that they can then control.
A jealous rival of Inuyasha might kidnap Kagome. For example, another demon who wants Inuyasha for himself might think that by taking Kagome, he can get Inuyasha to do his bidding. This would create a lot of drama and conflict between Inuyasha and the kidnapper.
It could also be a lone vampire with a vendetta against Kaname or the academy. This vampire might think that by kidnapping Yuki, they can exact revenge on Kaname or cause chaos within the academy. Yuki is an important figure in the Vampire Knight world, and her kidnapping would surely disrupt the delicate balance that exists.
One likely kidnapper could be Discord. He loves chaos and might see kidnapping Twilight as a great way to create chaos in Equestria. He could be bored and think that Twilight's absence would disrupt the harmony that she and her friends usually maintain. Another possible kidnapper is a jealous rival magician. Someone who is envious of Twilight's power and knowledge of magic and believes that by kidnapping her, they can steal her secrets and become the most powerful magic user in Equestria.
The Naraku would be a likely kidnapper. He is always plotting against Inuyasha and trying to get his hands on the Tessaiga. Kidnapping Inuyasha would be a way for him to either steal the sword or find a way to break Inuyasha's spirit so that he can no longer oppose him.
The Joker is a likely kidnapper. He has a history of causing chaos and targeting the Bat - family. He might see kidnapping Batgirl as a way to get back at Batman or just for his own twisted amusement.
In certain fanfictions, a jealous rival of Amy Rose could be the kidnapper. This could be another female character who has feelings for Sonic and sees Amy Rose as a threat. She might think that by getting rid of Amy Rose, she can have Sonic all to herself. Or it could be a character from Amy Rose's past who has some unresolved issues with her and decides to kidnap her to get revenge or make her pay for something that happened a long time ago.