Anakin would probably be a respected Jedi Master. He would be living in the Jedi Temple, training new padawans. His relationship with Obi - Wan would continue to be that of a mentor - mentee relationship, but also a deep friendship. He would be a loving father to Luke and Leia, teaching them the ways of the Force from a young age.
If Anakin didn't turn to the dark side in fanfiction, it's conceivable that he would have become a true hero. He could have trained more Jedi, passed on his skills and wisdom, and maybe even prevented the rise of new villains. The story would be filled with hope and optimism instead of the darkness that followed his fall.
Well, if Anakin didn't turn to the dark side, the Clone Wars would probably have ended differently. Anakin was a key figure in many battles during the Clone Wars. His continued loyalty to the Jedi could have meant a more decisive victory for the Republic. The Sith plot to create the Empire through the Clone Wars would have been foiled. And the relationship between the Jedi and the clones might have evolved in a more positive way. Anakin could have used his influence to improve the treatment of the clones, and they could have become an even more integral part of the Republic's defense force rather than being turned against the Jedi as they were when Anakin turned.
In such a fanfiction, Anakin would likely remain a Jedi. He would continue to fight for the Republic and the Jedi Order. He might have a more positive influence on the Clone Wars, perhaps finding a way to end the conflict more peacefully. His relationship with Padmé would also be different, not marred by his fall to the dark side.
In fanfiction, Anakin joining the Dark Side often has complex motives. It could be due to his fear of losing Padmé. The Dark Side might seem to offer him a way to save her, so he succumbs to its power.
Betrayal is also a big theme. He betrays the Jedi Order, his friends, and ultimately himself. His relationship with Obi - Wan, for example, is often explored in these fanfictions as a relationship that is shattered by his turn to the dark side. And there's the theme of internal conflict. Anakin is constantly at war with himself, his good side fighting against the allure of the dark side, which is a central aspect in many of these stories.
Fanfiction usually develops Anakin's character by showing his relationships in a new light. His bond with Palpatine could be shown as more complex, with Palpatine slowly manipulating Anakin over a long period, preying on his weaknesses like his desire for power to save Padmé. This makes his turn seem more gradual and believable.
If Anakin hadn't turned, the Sith's plans might have been foiled. The balance of power would have remained with the Jedi, and galactic conflicts could have been avoided or resolved differently.
Well, the galaxy would have been a much more peaceful place. The Jedi Order might have remained strong, and there would likely have been no rise of the Empire.
Perhaps a fanfic that delves into the time when Anakin was on the cusp of turning to the dark side. Padme could sense the change in him and tries to prevent it with the help of Luke and Leia from the future who somehow travel back in time. This would create a complex web of relationships and a race against time to save Anakin from the dark side.
Another plot is Anakin's search for greater power in fanfiction. He believes that the Jedi Order is holding him back from reaching his full potential, and the Dark Side seems to offer unlimited power. So he makes the fateful decision to join it. This often involves his internal struggle between the light and the dark within him, which is a great source of drama in these fanfictions.