To Have and Have Not

In order to decide if slavery still exists, first one needs to define "slave".
If it is decided that slavery is to own another person the way one owns a dog, then no, there is no slavery, only bondage.
But if you define slavery as working a person in harsh conditions for very little pay and not letting them leave your employment, then we have a problem. It is well known that lots of people come to America with hopes and dreams of a bigger and better life. What's probably not so well known (or at least not as much talked about) is what really happens to those hundreds of people who find themselves working for someone on farms, in factories or out on the streets.
Maybe they owe this person something. Maybe their boss has threatened them with deportation if they leave to find a better job. Whatever the reason, these immigrants, runaways, what have you, are trapped in a viscious cycle. Putting their health, even their lives in danger just to make enough money for food and a roof over their heads (and maybe their coke habit, but that's a whole-nother issue).
In that way, slavery is still running strong in the Land of the Free. Ironic, huh?