Detective Joe Bourquin is one of the first characters we get to see in Watchmen, after Rorschach's opening narration.
He and Detective Steven Fine are the policemen who investigate Edward Blake's murder, but decide to let it "drop out of sight" out of fear that they'll have to deal with Rorschach's intervention. They also investigate some other cases throughout the novel.
Joe also helps Steve to try and capture Daniel Dreiberg, but he escapes and Steve is suspended. Joe is with him in a type of police cab/car (that might be taking them home) and they both eventually die by the psychic wave.
While Steve seems to have a more rebel attitude towards the cases and his job (you could say the bad cop or the "cool" cop) Joe seems to be more like the worried boss, trying to get the job well done.
Joe also mentions that he has astrological beliefs, as noted in the case of Mrs. Hirsch.
In the Movie Joe and Steve have minor appearance. Zack Snyder explained that they might be dealing with something bigger than them both.