User blog comment:San&Ashitaka/Levi!/@comment-179280-20131024175832/@comment-1971498-20131025152206

I don't see his "importance" as being the reason for his popularity. While a lot of his popularity comes from being a "badass", pushing that aside, Levi does hold certain qualities that makes his character very likable, as outlined by Dave55811 in the following:

I do have to give Levi some credit, though. Despite his archetype, he does have sort of a compassionate side....the first example would be that he assures a dying comrade that his death wasn't in vein. This shows that Levi isn't a total dick-head.

Also, one of his quotes is something more people ought to live by, that "I don't know which option would you choose. I could never advise you on that...no matter what kind of wisdom dictates you the option you pick, no one will be able to tell if it's right or wrong until you arrive to some sort of outcome from your choice," and thus, "The only thing we're allowed to do is to believe that we won't regret the choice we made." Most anime/manga characters tend to have these epic quotes of sorts, but Levi's is very realistic in comparison.

Plus, despite his tsundere ways, one significant quirk about him is his sense of cleanliness. This makes for humorous insinuations; he's supposed to be this bad-ass but then "Oh my God everything's dirty!" and he rushes to fix it up. xD

Despite his brooding nature and his seeming apathetic attitude, what makes his character appealing is his deep sense of camaradery. He's touted as "humanity's strongest" and displayed almost as a snarky and merciless soldier. Despite all that, he's slowly revealed to the audience as having a deep sense of compassion and respect towards his men unlike any other character that's been shown in the series.

Levi may not be one of my top faves (he's a fave of mine but it's not like I'm crazy for him), but I can definitely see why he'd have serious fans as well (beyond those who simply like him for his prowess and fighting skills).