A person should change their tires when the tread becomes less than 1/16th of an inch. Once the tread wears down to this point, the tire can flatten or pop.
One easy way to check the tread depth on tires is to use a penny. Take the penny and insert it in the tread groove facing down. If all of Lincoln's head on the penny is visible, it is time to replace the tires. Good tread depth measures 1/8th of an inch" or more. Above 1/16th of an inch means that the tires will need replacing soon.