Yes, you should be concerned. If possible, use stainless steel or cast iron.
When recipes call for a non-stick pan, try substituting for cast iron or stainless steel. These durable alternatives serve the same purpose when used properly. There are many coatings and materials marketed as healthy alternatives to non-stick, but cast iron and stainless steel are time-tested and proven to be safe.
If you already own non-stick cookware, cook at low temperatures and never pre-heat an empty pan to prevent overheating.
Most non-stick pans give off fumes under high heat. Avoid the risk of polymer fume fever.
In only five minutes, a non-stick pan coated with Teflon® (polytetrafluoroetheylene) can give off fumes that cause polymer fume fever and kill pet birds. Symptoms of polymer fume fever include discomfort in the chest, dry irritating cough, shivering attack, sweating and general malaise.
The chemicals used to manufacture non-stick coatings harm human health and the environment.
Perfluorinated compounds (PFCs) are a class of chemicals used to make things non-stick, stain resistant and waterproof. Some microwave popcorn, fast food wrappers and other unexpected products utilize these chemicals’ slippery properties. Unfortunately, PFCs and their breakdown products accumulate in the environment and your body and may cause abnormal thyroid hormone levels and reduced immune system response.
Environmental Working Group's research on heathing non-stick pans
DuPont's cooking safety tips for bird owners
National Institute of Environmental Health Sciences background information on PFCs
Huffington Post article on PFC health consequences
New York Times article on the advantages of cast iron pans