Talcum powder consists of finely ground magnesium silicate. Zinc and magnesium stearate may be present as well.  Nowadays, talc is found in a lot of consumer products. Many varieties of baby powders still contain talc as their principal ingredient.

Scientists have found striking similarities between talc particles and asbestos. In 1993, a National Toxicology Program report found that talc, without any asbestos, caused tumors in animals. Testing has not been done with humans. So, cosmetic grade talc is still not regulated by the government.
The U.S. Food and Drug Administration (FDA) considers non-asbestiform talc, that is talc which does not contain potentially carcinogenic asbestiform amphibole fibers, to be Generally Recognized As Safe (GRAS) for use in cosmetics. Scientists are still researching the link between talc and ovarian cancer. This is because women apply talc in their groin area. No conclusive report has been prepared by anyone, and the link still has not been established.

As of now, there is no hard evidence to suggest that talcum powder causes cancer in babies. However, if the baby inhales talcum powder, that is definitely dangerous. If you want to be on the safe side of things, use baby powders which are based on non-talcum ingredients, like corn starch.