Well, Naruto could use his telekinesis powers in combat. He might be able to disarm his opponents without even touching them. Just by using his mind, he could send their weapons flying. For example, against Sasuke, he could stop Sasuke's sword attacks mid - air and then take the sword away from him. It would be a huge advantage in battles.
Well, if Naruto gets Shinigami powers in a fanfiction, he could potentially gain the ability to manipulate souls. He might be able to use the Shinigami's scythe in combat, which would be a really cool and unique weapon. Also, he could have new forms of jutsu related to the soul realm.
His relationship with Sakura might change. Sakura would be even more impressed with Naruto having this new power. She might see him as an even greater ninja and could potentially develop stronger feelings for him. Naruto, on the other hand, might use his telekinesis to do small things for Sakura, like picking flowers for her without having to touch them.
Well, Naruto getting the Seven Deadly Sins powers would likely change his relationships. His friends might be a bit wary of him at first, especially if he got the power of Envy. He could start to envy others' skills or powers in a way he never did before. But on the other hand, if he had the power of Kindness (the opposite of some of the sins), he could use it to bring out the best in his friends and foes alike.
His powers would change a great deal. Naruto is known for his brute strength and his ability to never give up. The Sharingan would add a whole new layer of finesse to his fighting style. He could use the Sharingan's genjutsu capabilities to trap his enemies in illusions before hitting them with a powerful chakra - infused punch. Also, he could use it to analyze his opponents' weaknesses more quickly, allowing him to adapt his fighting strategy on the fly.
Well, he'd probably be even more of a badass. His already formidable combat skills combined with Wolverine's healing factor and adamantium claws would make him nearly unbeatable. He could take on stronger foes without worrying much about getting hurt. And his speed and agility from his ninja training, along with Wolverine's berserker rage, would create a really interesting and powerful character in the fanfiction world.
Well, Naruto would become extremely powerful. His combat abilities would likely be enhanced with the unique powers of arrancars. He could gain new forms and techniques. Maybe he'd have a zanpakuto-like weapon with special abilities, which would add a whole new dimension to his fighting style. Also, his speed and strength might increase exponentially, making him even more of a force to be reckoned with in the Naruto universe.
Well, he might become even more powerful and be able to transform into new and amazing creatures. Maybe he could gain the ability to fly in his animal forms, which would be really cool.
Well, Dipper might start causing chaos just like Bill. He could use his new powers to play pranks on Mabel, like turning her sweaters into strange, living creatures. Or he could use the power of mind - reading to know what everyone in Gravity Falls is thinking, which would lead to some really awkward and funny situations.
Some fanfictions might give Naruto the power of elemental fusion. He could combine fire, wind, water, earth, and lightning in ways that are not possible in the original series. This would make his attacks extremely powerful and unpredictable. For instance, he could create a storm of lightning - infused water that not only electrocutes his enemies but also drowns them.
In a 'naruto gets captured' fanfiction, he might be tortured for information. His captors could be after the secrets of his Nine - Tails chakra. They may try to use him as a bargaining chip against Konoha.