Shamus Young said:
Stolen Pixels #160: Rorschach Interview, Part 2
The most reprehensible of the Watchmen is also the most popular. Why?
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In most simple terms, a lot of people like him because he's a bad ass. He is not only physically capable, but he is merciless. People see him more as a warrior.
I like him for various reasons. I think a few people may have just the right political or philosophical alignment to agree with some of what he says. I may be a political moderate, but at the time I read the comic I was in College and surrounded by loud-mouthed liberals whose ignorance was as broad as the red neck spouting idiotic hate on Obama. Hence Rorschach's opening monologue got me all giddy to read, because while it's not necessarily correct it isn't necessarily wrong either. Thus from the start Rorschach becomes a character we can like.
Also, that first issue does a lot for the story as well. As you can see from the comments, people mistake him as being the protagonist. In truth, he's merely there to kick start the narrative. He's not the protagonist, and if you were to try and pin point one you'd probably have trouble. I'd say Nite Owl is the closest thing to the hero of the story, but even that is debatable.
In an interview Alan Moore confessed that Rorschach was supposed to be a hated character due to being such an extremist. However, deep down inside all of us wish we could take extreme measures once in a while. Not to mention that it becomes revealed that Rorschach wasn't always like this. He even says he used to allow criminals to live. It's only when he is confronted by a crime so horrific that he finally and truly snaps, seeing the flaw in the system. While a character like Batman (who Nite Owl is more a reflection of) refuses to kill, believing that the system CAN work, Rorschach feels it doesn't. The criminals just deal with it until they can get out and do it again. So Rorschach finally snaps and does the only true solution: to kill them.
It's not repulsive or reprehensible. It's something we can all understand. By allowing readers to see that Rorschach is so messed up because 1) a fucked up childhood, and 2) his naive ideals being torn away by a most horrific crime, we can see the human inside of him being torn asunder until he becomes what we see in the comic. A once hero that no longer believes in the system of justice, especially since they don't hold up to his own high expectations.
By being so extreme Rorschach becomes the most interesting of all the characters. And there comes the deeper reason he resonates with fans. Not everyone thinks this hard about it, and many still hate him, but a lot of people like him because 1) he's a bad ass, and 2) he's the most interesting psychologically of all the heroes.