I believe most people like him for his complexity and that he is truly the most dynamic character in the series.
Out of the typical polar characters of the manga, Obito has been at the most extreme ends of both sides (Will of Fire vs Curse of Hatred, Yang and Yin, etc). He has had the immovable Will that Naruto represents at his younger years, and had the manipulative and cynical Will of Madara at his later years. His childhood speech (as close as I remember) outlines the motivations of both the protagonists and antagonists of the story even: "...Those who abandon their friends are worse than trash. And if I am to be trash, I'll break the rules. If that's not a true shinobi, then I'll crush that idea of a shinobi."
What most characters in the series represent with their Yin/Yang rival/counterpart, Obito has represented the will of both the protagonist and (main) antagonist through his character alone, not through bonds. He's just all around cool, and serves as a huge crossroads character for almost every major theme in the manga.
Also, misconception: He did not do this because of Rin, she was merely the catalyst. It was because he wanted to deny reality. He wanted a world where people would not have to endure injustices and painful changes such has this event. He didn't want to endure the hardship, so he denied everything seeking to crush the idea of what a shinobi is, attempting to "end" the world. In the process he denied himself, his friends, his dreams, and ironically ended up enduring more hardship in the end. His sharingan ability even allows him to "run away" from the real world, to where he doesn't even have to acknowledge enemy attacks.
^^ This is also why he didn't just kill Naruto. He wanted to either crush Naruto's Will, or be moved by it. Either way, it would reaffirm his "crossroads."
In my experience, the people that like Obito can appreciate these complexities that Kishimoto has worked so hard building. He's a symbolic kind of character, representing the ideologies and major themes of the manga.
For those that don't like him, that's fine. Kishimoto's intention is to make him unlikable. Good guys hate him, bad guys hate him, he's alone, he's tragic, he brought it on himself. He's the failed version of both the protagonist (he's anti/dark Rikudou), and the antagonist (he ensured the protagonist's victory through holding back as the villain).
That is why I like Obito. His design is tragically perfect and is the best support character of the manga's themes in every way.