It varies by state. Some states dont allow collections of old debt more than 3 years old. If you acknowledge the debt in that time period the clock restarts.
A debt should be reported for seven years, but the debt can be sold for collection and reported at a later date extending the time on your credit report.
The statute of limitations varies from state to state and according to type of debt. Generally, it is 3-10 years. Google "statute of limitations on debt" for more specific info.
There are varying statutes for different kinds of debt (medical/credit card/etc) and those vary by state. There are several online sites that detail the SOL for each type of debt.
It really depends on what state you live in. Every state has different laws. It also depends on what the bill was for but I would say after 10 years it is pretty safe to say they can't touch you but check with your state for the laws.