That's why I was shocked to learn that you can't burn just about anything in them. Get our free mobile appI knew this within reason but I was not aware that you couldn't burn your everyday household trash. If you aren't entirely sure what you can and can't burn, just stick to firewood. Getty Images City Officials Could Approve Ban On Beach Fire Rings At Some California BeachesThe Minnesota DNR says burning of household trash has been illegal since 1969. In this case, those households are allowed to burn some household trash while following the proper guidelines.