There's a long unpleasant history of attempts at eugenics -- for much of the twentieth century, the US government sterilized some American Indian women, for instance, and sterilization of the "feeble-minded" was common in a lot of Western countries until relatively recently. I think generally social attitudes have swung around to most people agreeing that eugenics is maybe not that great a thing, so you don't really see much of this anymore in the West.
What are the limits of this, though? Is direct control of people's reproductive abilities just something that should always be outside of the purview of the State? Would it be reasonable for the State to require sterilization of, say, people who abuse or neglect their children (to avoid giving them more potential targets)? Or people who reproduce despite being on public assistance? Would it be okay for the State to require some sort of long-lasting birth control or reversible sterilization as a condition of providing welfare?
In sum, my question to you guys is this: what are the circumstances in which the State may extend its tentacles (so to speak) to restrict people's ability to procreate?