It could be out of loyalty to the wizarding world. Harry is seen as an important figure in the fight against the dark forces. Fleur realizes that Harry's safety is crucial for the future of the wizarding community, so she saves him from the Dursleys who are a threat to his well - being in a different way compared to the dark wizards.
Well, perhaps Fleur uses her Veela charm to intimidate the Dursleys into letting Harry go. She could arrive at Privet Drive in a blaze of magical beauty and power, and the Dursleys, being the cowards they are, would be too scared to oppose her when she demands Harry come with her.
Fleur could be shown as more independent and brave. Since she's taking it upon herself to save Harry, it shows her courage. Maybe she becomes more confident in her own abilities outside of the Triwizard Tournament context.
Love for Lily. Since Harry is Lily's son, Snape might feel an obligation to protect him. He couldn't save Lily, but he can try to keep her son safe.
Well, it could be that Draco has a change of heart early on. He realizes that the Dursleys are truly awful to Harry. So he uses magic to create distractions. He could make strange things happen around the house that scare the Dursleys so much that they just want Harry to leave. Then Draco could be waiting outside and whisk Harry away to a safer place, like a hidden place in the wizarding world where he has set up a little haven for Harry.
There are many ways it could be written in fanfiction. Ginny might use her knowledge of the wizarding world and Hogwarts' secrets. She could use a special spell that she learned from an old book in the Hogwarts library. This spell could create a portal right inside the Dursleys' living room that only Harry can see. Ginny could then communicate with Harry through a magical device, tell him about the portal, and he can use it to escape from the Dursleys. Ginny would have to be very careful and plan everything precisely to avoid detection by the Ministry of Magic, as using magic around Muggles without permission is strictly prohibited.
In some fanfictions, Fleur might use her Veela charm to intimidate the Dursleys into letting Harry go. The Dursleys, being easily cowed by the extraordinary, would be no match for Fleur's alluring yet powerful presence.
One possible motivation is a sense of morality that Draco has buried deep inside. Despite his upbringing in a family of Death Eaters, he still has a conscience. Seeing Greyback about to harm Hermione, who is essentially an innocent in the face of such a brutal werewolf, stirs that conscience. Another factor could be his own self - interest. He might realize that by saving Hermione, he could gain some sort of leverage or protection in the complex world of the wizarding war.
Love. In fanfictions, it's a common motivation. Draco might have fallen in love with Hermione over time, and that love drives him to risk his life to save her from Voldemort.
Well, in some fanfictions, Bill might use his magical skills and knowledge. He could cast spells to create distractions for the Dursleys, allowing Harry to escape unnoticed. For example, he might make a flock of magical birds fly into the Dursley's yard, causing chaos while he smuggles Harry out.
Snape might be motivated by a desire for redemption. He has a complicated past, and saving Harry could be his way of making up for all the bad things he has done or been associated with. Additionally, he might see a bit of himself in Harry's situation, as he also had a difficult childhood, and this empathy drives him to act.