Naruto, as an anime, has a lot that makes it memorable. From its relatable characters to its memorable messages about never giving up, much of what this series does sets the standard for what makes a successful shonen manga. However, if one were to be asked what they remember best about Naruto, the rivalry between the two main characters would likely come up.
The rivalry between Naruto and Sasuke is one of the most iconic in all of shonen anime. A surprising amount of Naruto's character arc revolves around his ability to deal with his rival. On top of that, Sasuke manages to surpass the base requirements of a rival character to become something truly his own. Despite that, however, the two characters are intertwined by the overarching themes of the story and have more to do with each other than even the narrative makes apparent. All of these elements and more go together to make this rivalry truly unforgettable.
Part of what makes this rivalry so memorable is the theme of effort that it embodies. To paraphrase Rock Lee, there are two ways to get good at something-- natural talent and back-breaking labor. For the most part, Sasuke embodies the former and Naruto the latter. A lot of people resonate with the idea of working hard to succeed or excel at something, which is what helps them feel connected to the way these characters develop.
Sasuke also works well as a rival character in the ways that he grows beyond his role in the story. Normally, a rival character is either someone the main character needs to surpass or someone who will always try to be one step ahead of them; their stories end up closely intertwined because of this. Sasuke, on the other hand, manages to make his story branch off from Naruto's, and thus the two are able to learn and grow in far different ways. Their stories are still ultimately connected, but Sasuke feels much more like his own character with his own story that just happens to run parallel to Naruto's.
It's also interesting how each of these characters is similar in their rate of development. Each of them gains a new power-up at around the same time; if Sasuke learns the Chidori, Naruto learns the Rasengan; if Sasuke gains the Mangekyo Sharingan, Naruto masters Sage Mode; if Naruto gains the power to manifest the Nine Tails as an energy giant, Sasuke learns to do the same with his Susanoo. Throughout the series, both of them acquire cool, new powers that let them stand on equal ground in their final battle.
On a deeper level, Naruto and Sasuke's rivalry is fascinating in how it reflects the themes of the narrative. Both of these characters are regularly subjected to the pain and hatred that exists in the world and come to realize how it's been perpetuated over the course of history. A big part of their individual stories is learning how to deal with that hatred.
Of course, due to their differing experiences, Naruto and Sasuke reach far different conclusions about dealing with hatred. Sasuke started off by coming to learn the pain of loss and the frustration of not being able to avenge that loss. He might have overcome his pain with the help of friends, but then he wouldn't have had the strength to avenge his clan. Throughout his journey, he gains a clearer understanding of how awful the ninja world really is and seeks to reform it. He resolves to alter the cycle of hatred by becoming both an insurmountable source and an unavoidable target for it.
Naruto takes a slightly different road, which leads him to a different conclusion. He started off knowing the pain of isolation, but he learned to overcome it with the love and acceptance of the people in his life. He also learned to understand what it means to lose something and become frustrated and hateful like Sasuke. However, with the help of those around him, he overcame that hatred and sought to make the world a better place; to him, this is part of what it takes to become Hokage. Therefore, becoming Hokage and finding out what to do about Sasuke's hatred are one and the same.
The difference in how Naruto and Sasuke seek to resolve these issues is at the center of their conflict, which is their final battle. Sasuke believes that he needs to rely on his individual strength to rise above everyone else and become the one place for them to direct all their hatred. Naruto, however, knows that trying to bear the weight of the world is an impossible task and that people need companionship to persevere. Sasuke wants to sever ties and discard the history of hatred, but Naruto wants to embrace them and learn from them. Their different ideas of how to save the world from hatred are what ultimately force them to confront each other.
Going back to the simple, the epicness of Naruto and Sasuke's rivalry is cemented by its amazing fight scenes. It's rare, but when these two fight, it's one of the greatest spectacles to come out of the series. Their final battle is especially brilliant in its presentation and execution. Naruto, in general, has some well-done fights, but this one really went above and beyond to be the series' ultimate final battle.
All of these things and more have made Naruto and Sasuke's rivalry one of the best in all of anime. Some audiences like to mock these two for yelling out each other's names or having some secret romance, but if they weren't so memorable to begin with, not many would care. The quality put into the story between these two is what truly makes it great.