Sasuke could be acting out of jealousy. He might have seen Sakura getting closer to someone else, like another ninja in the village, and in a fit of rage and possessiveness, he kidnaps her. Or it could be part of a test. He wants to see how the Hidden Leaf will react, or more specifically, how Naruto will react. By kidnapping Sakura, he creates a situation that forces Naruto to come after him, which could be part of some larger plan in Sasuke's mind.
One possible motive could be that Sasuke is being controlled by some dark force. Maybe an enemy has a hold over him and is using him to kidnap Sakura as a way to get to Naruto or the Hidden Leaf Village. Another reason might be a misunderstanding on Sasuke's part. He could think that Sakura has some information that is crucial to his personal vendetta and decides to take her by force to get that information.
One possible motive could be to use Sakura as bait. Maybe Sasuke is trying to lure Naruto to a certain location. He knows Naruto cares deeply about Sakura, so he figures Naruto will come after her.
One possible motive could be his thirst for power. By kidnapping someone with a special ability or knowledge, like a powerful Force - user or a brilliant scientist, he could gain an edge in his quest to rule the galaxy. For example, if he kidnapped a Jedi who knew the location of ancient Sith artifacts, he could use those artifacts to increase his own strength.
One possible motive could be to protect Sasuke. Itachi might have seen a great danger approaching Sasuke that he could only avoid by taking him away forcefully. Maybe there was a powerful enemy targeting Sasuke, and Itachi thought that by kidnapping him, he could keep him safe in a hidden location and train him to become stronger.
One possible motive could be his fear of losing her. In the Star Wars universe, Anakin is deeply in love with Padme. If in fanfiction he feels that she is in danger or might be taken away from him by some external force or person, his desperation could lead him to kidnap her in an attempt to keep her safe. For example, if he suspects the Jedi Council of having some secret plan regarding Padme, his unstable state of mind might push him to this extreme action.
Well, Ursula could kidnap Ariel in fanfiction because she wants to take Ariel's place. Think about it. Ariel has a loving family, a great voice, and is adored by many. Ursula, on the other hand, is often shunned. So she might think that by kidnapping Ariel and getting rid of her, she can step into Ariel's life. Maybe she wants to be the one who is loved by Prince Eric. Or perhaps she wants to be the favorite daughter of King Triton. It's all about her twisted desires for a different kind of life.
It could be that Peter has some sort of knowledge or information that the kidnappers want. For example, he might have accidentally witnessed a crime and the criminals want to keep him silent.
A possible motive could be a creative exploration of the 'what - if' scenarios. Maybe the writer wants to see how the story would unfold if Sasuke completely lost his way. Another motive could be to create a sense of high - stakes drama. Since Sakura is an important character, her death at Sasuke's hands would be a huge shock.
One possible motive could be power. Damon might see Elena as a pawn in his game to gain more influence in the supernatural world. He could think that by kidnapping her, he can control those who care about her and make them do his bidding.
Perhaps in the fanfiction world, Naruto has lost his sanity for some reason. Maybe he has been through a traumatic event that has warped his sense of right and wrong. Hinata, being someone he cares about deeply, becomes a target of his deranged actions. However, this would be a very dark take on the Naruto - Hinata relationship, and often such fanfictions use this extreme situation to then explore how Hinata might be able to bring Naruto back to his senses, or how the other characters in the Naruto universe would react to such a situation.
Sasuke might want to get some information from Naruko. Maybe he suspects that she knows something about a threat to the Uchiha clan that he is trying to uncover.