Rorschach is an interesting character to me because I don't think we were supposed to like him as much as we do. He's easily the most popular of the Watchmen, but at the same time he's the most reprehensible. In some ways he's what Batman would be like if he was broke. And a complete asshole.
Rorschach is abusive, paranoid, homophobic, self-righteous, and exceptionally violent. Most of the rest of the Watchmen are crazy in their own way, but overall they're nicer and more well-adjusted than Rorschach. In their personal lives they seem more or less like normal people. Rorschach doesn't even seem to have a personal life.
I don't think author Alan Moore intended for him to be well-liked, but that's how it turned out. People are repulsed by Rorschach's behavior, but impressed with his fearless tenacity and sense of duty in the face of an entire generation of heroes who simply gave up.
Shamus Young is a programmer and writer by trade, videogame nitpicker by inclination. If you have the patience for more of his ramblings, they can be found here.