Throughout the series of Naruto, there are many rivalries between characters. Below you can find information on some of the main rivalries that extend throughout the series.
Naruto & Sasuke
Since the moment they saw each other in the academy; they've despised each other. Sasuke was popular with all the girls and didn't care, Naruto wasn't popular with any of the girls and did care. Naruto always thought Sasuke was trying to show off and Sasuke was basically annoyed with Naruto until he saw him in his first true battle with Zabuza. Then Sasuke acknowledged that Naruto wasn't just an annoying ninja and gained a little more respect for Naruto. Now instead of just resenting Naruto, he made it his goal to defeat him. Naruto and Sasuke train intensively to beat each other in combat.
Gai & Kakashi
Since they were in the academy, these two current Jounins have been fighting to top the other. Their record in any kind of competitive game, match, or whatever (which include games of "Rock-Paper-Scissors"), is 49-50, with Gai in the lead by just 1. Their rivalry is quite intense and they are constantly holding various competitions, which range widely, to see who is the best. Another way they express their rivalry is through their team of Gennins. Whenever their pupils go into battle with each other; they urge them on to beat the other because of their rivalry. Many times however, this rivalry is used for comical purposes.
Ino & Sakura
When these two were in the ninja academy, Ino was a more popular girl who helped Sakura gain more confidence in herself and become better at many things. They were best friends and got along really well. But then they both found out that the other liked Sasuke. Because of this, they became rivals, debating who would win the love of Sasuke. Their greatest battle was in the preliminaries of the 3rd part of the Chunnin Exam and it was a tie. During the fight, they stated that this fight wasn't about Sasuke and each of the Shinobis showed their true power.
Neji & Rock Lee
Although this rivalry is not as obvious and doesn't show as often as others, it is there. Neji believes that when a person is born, their fate is decided and cannot be changed. Rock Lee believes that through hard work, anyone can persevere. Rock Lee has always wanted to defeat the genius Neji, but Neji doesn't really accept Rock Lee as being a good Shinobi until Lee's fight with Gaara.
Orochimaru & The Akatsuki
Ever since Orochimaru left The Akatsuki, he has not been looked upon kindly by the members of Akatsuki. Orochimaru has been tracking down the location of The Akatsuki along with his right hand man Kabuto. He met with Sasori and was planning on killing him after finding Akatsuki’s location.