The health concerns associated with nonstick cookware have to do with a chemical called perfluorooctanoic acid (PFOA) that is used to bond the nonstick coating to cookware. In 2005, the Environmental Protection Agency (EPA) labeled PFOA as "likely to be carcinogenic to humans." Studies by the European Food Safety Authority (EFSA) show that high exposure to PFOA “can have a harmful impact on health and can damage the liver, cause developmental and possibly reproductive problems.” Not good news considering PFOA is present in the bloodstream of 9 out of 10 Americans and in the blood of most newborns.
Before going any further, it's important to note that nonstick cookware is not the sole exposure source of PFOA. Furniture, cosmetics, household cleaners, clothing, and packaged food containers can all contain Perfluorinated Compounds (PFCs), many of which break down into PFOA in the environment or in the human body. Some of the most popular PFC brand names are Teflon, Stainmaster, and Scotchgard. Check out the Environmental Working Group's Guide to PFCs to learn more about the health concerns associated with PFCs and how to avoid them.
Ask for nonstick cookware and PFOA, there are measures you can take to avoid or at least reduce the amount of PFOA being released. First, only use nonstick cookware with medium heat (350 to 400 degrees Fahrenheit) or lower. Add water or oil to cookware to absorb heat before turning on a burner or the oven. Wash nonstick cookware by hand using nonabrasive cleaners and sponges and avoid using metal utensils or stacking pots and pans to avoid scratching. If any of your nonstick cookware does become scratched, toss it or (for a slightly more eco-friendly option) bring it to a scrap metal yard.
You can also rotate out any nonstick cookware with pieces made from other materials. Health Canada has a great overview of the benefits and risks of various cookware materials. I think it's best to have an assortment. Personally, I use stainless steel pots, a cast iron skillet (this is my go-to cookware piece), ceramic and Pyrex baking dishes, and silicone bakeware.
Just be wary of the “green nonstick” products currently on the market. In 2006, the EPA and eight major U.S. companies, including Teflon-maker DuPont, launched the 2010/15 PFOA Stewardship Program, where the companies committed to reducing their use of PFOA and related chemicals by 95 percent by 2010, and to work toward eliminating it completely by 2015. To meet these deadlines the companies rushed to market replacement chemicals they claim are safer. These new chemicals, known as C6 chemistries, are a lot like PFOA (also known as C8) in that they persist in the environment, are extremely toxic to aquatic life, and can cross the placenta to contaminate babies before birth. Unlike PFOA, there is practically no information on their health risks. I'd steer clear until more information becomes available.