How long can credit card companies legally continue to harass someone about an old debt?

Your question concerns the applicable statute of limitations, if any, and perhaps consumer protection issues.  First, as to how long the creditor may attempt to collect the debt, it depends on the applicable statute of limitations.  Since a statute of limitations is a procedural right, you want to check with the law of the state in which you are likely to be sued, which is usually the state you live in (under the National Bank Act, the law of the state in which the bank maintains its "principal" office governs, and most credit card agreements contain a forum clause requiring suit to be brought in the state in which the bank is located; however, it is my experience that the bank will usually sue the person in the state in which they live).

Once you figure out the applicable statute of limitations, then you apply that to each individual charge.  In other words, if the statute of limitations is three years, and all your charges were more than three years ago, you are safe.  If the limitations is three years, and two charges were more than three years ago, but another two were last week, then you may be sued for the two charges last week, but not the ones from more than three years ago.  In other words, each individual charge starts its own separate and individual limitations tolling period.

Now to the consumer protection issue.  Most states have consumer protection statutes that prohibit, among other things, misrepresentations in the collection of consumer debts - like credit card debts.  If the debt collector said there is a judgment against you that you have never heard of, there is a good chance the collector is lying to you in an attempt to scare you, because there are strict court rules requiring notice to a person before being sued.  In other words, if there were a judgment against you, you would probably know it.  So, you may want to speak to consumer protection lawyers about whether the collector lied and you have rights under your state's consumer protection statute, if any.