From what little I've read about current slavery, it seems to be a function of unchecked power and greed over necessity or blindness. We in the U.S. don't think of Illegals working in fields or brothels as slaves, but they may be giving all their earned money to their handler (read: pimp) and working in extremely poor conditions. It's not classical slavery as we understand it from our textbooks, but the base factor -- people as product instead of individuals -- remains.
In other countries, slavery continues because no one has stepped up to stop it. It took a civil war just to start the road to abolition in the U.S.; elsewhere the governments never even considered an equal-rights-based system, and so the movements have trouble generating enough steam to continue.