Last week's f2f sci-fi discussion group was a golden oldie: Isaac Asimov's Caves of Steel. It's the first of three detective stories involving the collaboration of a human and a robot. It's a fairly played detective story, but it also involves a lot of social issues. The earth has become grossly overpopulated (at 8 million!) and is existing in enclosed underground cities, where the size of your small quarters depends on your job standing, everyone uses community bathroom facilities, and you are mostly eating processed yeast. The thought of going outside these enclosed spaces (the caves of steel) is scary for everyone. People have emigrated to other planets where there is plenty of room, but further emigration has been banned. Robots are taking over some human jobs, and are much hated for this.
With this background, the policeman Elijah Bailey has been detailed to solve the murder of a diplomat from one of the outer worlds, with all sorts of touchy political implications, and he has been given a "spacer" sidekick who turns out to be a robot. Bailey has to come to terms with his feelings about the robot and solve the murder, while avoiding a galactic incident.
There are two sequels. In The Naked Sun, Bailey travels to a sparcely inhabited world, where people only interact by video, personal contact being regarded as disgusting. Marriages are arranged by genetic suitability, and the mandated once a week personal interaction is endured stoically. (Since they're so scientifically advanced, I don't know why they don't just grow artificially produced embryos in bottles, but they don't.)
The third one, Robots of Dawn (which I haven't reread because I can't find it) somewhat resolves these issues, and holds out some hope for man's future. They all can stand on their own as detective stories.