Well he started off as an underdog, and people like to cheer for someone who has the odds against them. At first he didn't have a lot of skill, the only thing he had going for him was his massive supply of chakra thanks to the kyuubi. But he wasn't good at controlling it and wasn't a good learner. Then he had his rivalry with Sasuke that made him train harder and push himself to new limits. Him defeating the odds was satisfying to watch.
His positive attitude to never give up and never go back on his word, to support his friends no matter what, to succeed against a much stronger enemy, those are admirable traits. Slowly he turns the odds in his favor, and he's always fighting side by side with his comrades. He becomes stronger and stronger until he is no longer considered "talentless" by his peers. Eventually he is the most op character in his universe. Although he did have the "chosen one" privileges, we watched him grow and train to achieve his goal, which made him likable.
What a beautiful cat!