Canon Naruto pairings remain, to put it lightly, controversial. Some people love the relationships between Naruto and Hinata, and Sakura and Sasuke - but others wish it went down differently, many even shipping characters who the creators never planned for endgame relationships. That's where awesome non-canon ships come in - after all, a ship never needs to sail for it to have a real basis, or for it to interest fans. Whether you want to accept it or not, anime fans consider shipping to be a big deal, as evidenced by more than a few controversial anime ships.
Some of these ships are obvious - Yahiko and Konan being a couple is hinted at pretty heavily in canon, and Naruto and Sasuke are star-crossed lovers who would end up together if many fans had their way. Others get a little more creative - did you know that Kakashi x Iruka is one of the most popular pairings in the Japanese fandom, even though the two don't interact much? No matter what they are, non-canon ships are a great way to engage with the fandom and get your creative juices flowing.
Yahiko and Konan never get around to being an official canon couple, but it looks pretty obvious they care for each other deeply. The two are willing to go to war with Konoha together, putting their lives on the line to protect each other.
Their interactions heavily hint at romantic feelings, and if they were more than villains whose main appearances happen in childhood flashbacks and battle sequences, they might actually act on those feelings in the anime.
While this pairing feels canon, it's never officially stated, so it counts. Izumo and Kotetsu work together on nearly every mission they're assigned. In fact, they're so dedicated to each other that when Kotetsu undertakes a solo mission involving an ostrich, he nearly lets the ostrich murder him because he simply can't function without Izumo.
Izumo and Kotetsu is just one of those relationships that would be canon if it weren't part of a shonen anime from the early 2000s.
The relationship between Naruto and Sasuke emerged as probably the most popular one in the Naruto fandom, excluding the canon pairings. This happened for a reason - out of everyone Naruto encounters throughout the series, Sasuke receives the most of his affection. The titular character willingly risks his life to save Sasuke from getting himself killed in pursuit of revenge. He never gives up on him, and loves him unconditionally, even when he becomes an enemy of the state.
For Sasuke, someone who lost his entire family to a series of brutal murders, having someone always at your back no matter what proves invaluable. However you choose to interpret it, the love between these two is real.
Eventually, Karin will realize Sasuke doesn't reciprocate her feelings and turn her attention elsewhere - perhaps to another member of Team Taka, a ragtag group of escapees from Orochimaru's laboratory. Team Taka's initial goal involves helping Sasuke track down Itachi. Jugo is a little too serious for Karin, but she boasts a great dynamic with Suigetsu.
The two constantly trade sarcastic barbs, but beneath all the bickering lies genuine respect for each other as comrades and as people, and maybe even something more.