Cook with a burnt stainless steel pan and you risk burning the next meal as well. Stainless steel does not transfer heat well so, as a result, pots and pans have to be made with just a thin layer. Once they're burnt, the steel will warp and likely won't lie flat on your stove's burner. No matter how hard you try, the food won't cook evenly again.
Clean your scorched stainless steel with common cleaning supplies and you risk damaging the pan forever. If you scrub with stainless steel pads (such as SOS or Brillo or steel brushes, bits of the steel can stick to your pans, causing rust. Salt, which often used as an abrasive cleaner, is also dangerous for stainless steel pans, as it can leave permanent pits in the pan.
Burn your stainless steel pan and it is possible that the burned spots will leech nickel. Stainless steel is actually composed of small portions of nickel and chromium to help keep the pot from corroding. Most pots use a formula of 18/10 (18 parts chromium and 10 parts nickel). The FDA reports that food is our main source of nickel exposure.
Re-using your burnt stainless steel pans could also cause chromium to be leeched out. No study has been conclusive about how dangerous this actually is, but chromium, like nickel, is a known carcinogen.
The FDA considers glass, enamel and ceramic cookware to be safe. If you do use stainless steel, double check with the FDA website regarding recalls of stainless steel pans, since several well-known brands have been pulled.