Yes. It is called Human Trafficking. And it still happens all over the world. Not just 3rd world nations. Young, naive women are either tricked into going to a new country by promises of a better life, or, are just outright kidnapped. 
3 Things You Can Do To End Slavery

1. PREVENT:There is a well-documented link between physical poverty, length of education and slavery of all kinds. Poverty makes a child – any person – highly vulnerable to all forms of exploitation.One way to prevent slavery then is to combat poverty by meeting a child’s basic needs for education, proper nutrition, and health care. This is called holistic child development and the highest rated child development organization based in the U.S. is Compassion International. 
2. PROVOKE:A translator in the Dominican Republic told me that slavery will continue in that country until “we provoke companies to be fair.” Truth is that every time I buy clothes or produce from companies that do not treat workers fairly, I am rewarding bad behavior
 3. PRAY:Prayer doesn’t feel like substantive action does it? But if we believe the words of the apostle Paul, it certainly is.For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms. -Ephesians 6:12-