In 2013 the GEZ became the "Rundfunkgebuhr". The principal of this is very different in that it no longer relates to ownership or use of equipment, but is simply a flat charge per household. The legal standing of the charge remains questionable, but again many people (more than the GEZ) are happy to pay it. As with the GEZ many people continue to contest the viability of the charge and/or refuse to pay. There is little dispute that public media services have to be financed somehow, but the question remains if this is the best or fairest way to do it.
The German government support the enforcement of the Rundfunkgebuhr charge, but the legal status, especially for enforcement is dubious as it remains a private, rather than a public or governmental body. As with any private organisation, if they believe you owe them money (and that's all that is required), then they will take legal redress for you to pay. Threats are getting stronger and stronger, but so far there have been no tests in court for final enforcement. There continue to be legal arguments over the basis and application of the charge, or if it can be considered a "tax" and as such might be illegal in principal.
As threats get stronger more people are paying up. If ultimately the charge is accepted as legal (and that could be years away) then there will be legal enforcement on those that haven't paid, with additional charges for chasing the backdated debt.
There is no black or white answer as to if the charge is legal (or not). If you don't pay you will be hassled more and more. If you have a hard skin you may choose to ignore the letters and increasing threats. If the charge is finally determined to be legally enforceable you will be taken to court and made to pay (with additional costs and charges), or if you are no longer in Germany you'll be registered as debtor in the country should you return (a debt which they could potentially chase abroad). If it's not legally enforceable then there may be some alternative approach requiring you to pay, which may, or may not affect you, and may, or may not be backdated.