^^^No, not dead babies, from human embryos. The controversy is because you have to "destroy" the embryo, and some people feel that is destroying a human life. However, there is promising research being done using adult stem cells to recreate embryonic like stem cells. In which case, no embryo is being destroyed and therefore, no controversy.
The biggest controversy is that most people get their info about stem cell research from the Christopher Reeve episode of South Park. You don't crack open a baby and just drink from it's neck. And because of that, they go of an emotional decision, rather than looking at facts and statistics. Some say it's immoral to destroy an embryo... others say it's immoral NOT to do this research when it could improve the quality of many other lives. Who's right? Apparently God is always right, even to those of us that don't believe. And God hates science... because science keeps proving God to be non-existent the more we research.