Perhaps it's a case of being manipulated. In some fanfiction scenarios, dark side entities or Sith lords might manipulate Anakin into believing that kidnapping Padme is the only way to protect her from a greater threat. They could be using his love for her as a tool to drive him towards this immoral act, all while furthering their own dark agendas.
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.
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 his fall to the dark side clouding his judgment. He might think that by kidnapping Padme, he can protect her in his own twisted way. Maybe he believes the Jedi or other forces are a threat to her and he's the only one who can keep her safe.
One possible motive could be his complete fall to the dark side. The dark side twists his perception and makes him believe that Padme has betrayed him in some way, even if it's just a false notion in his corrupted mind.
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.
In some fanfiction set in a more peaceful time, they might interact with a lot of tender moments. They could have picnics and long walks, just enjoying each other's company and having deep conversations about their future.
A powerful crime syndicate could be responsible. They see Anakin as a valuable asset. Maybe they think they can sell him to the highest bidder, whether it's the Sith or some other powerful entity in the galaxy. They would use their extensive network of informants and thugs to carry out the kidnapping.
Obi - Wan Kenobi would be one. He's Anakin's master, and in the fanfiction, he might suspect something about their relationship and have to decide whether to support them or uphold the Jedi Code.
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.
Maybe Dumbledore believes that Harry has some hidden power that is being corrupted by the environment at Hogwarts. So, he kidnaps Harry to a secluded place to train him and help him control this power without any distractions or negative influences from other students or even some of the teachers.