The topic of safe cookware is somewhat controversial. For instance, some say stainless steel is safe, while others warn that acidic foods may cause toxic nickel, cobalt and chromium to leach into your food (read more about that in this article).
Aluminum. This is a highly toxic metal, linked to Alzheimer's and dementia among other conditions. Aluminum conducts heat quickly, which is why it's often used in cookware. The problem is aluminum also leaches very easily, especially when heated or exposed to acid foods (tomato soup, anyone?). Avoid cheap cookware made of aluminum. Now, some cookware has an aluminum core surrounded in a safer cooking material, and these may be an acceptable choice. But they carry a risk if the surface is damaged. Basically, you don't want your food touching aluminum, especially if it's heated.
Teflon/Non-stick. This is one of the most common types of cookware, but Teflon and other non-stick surfaces can release toxic fumes into the air when overheated (and how often have you accidentally left a pan too long on the stove?). And another trouble is this cookware scratches easily if you're not careful, so flecks of non-stick material can mix in unnoticed with your food. Plus your food is exposed to the metal underneath--most likely aluminum. So, non-stick cookware is a definite no-no.
SAFE COOKWARE (MAYBE)