The Zune Marketplace will close its virtual doors whenever Microsoft decides to flip the switch and convert from MS Points to local currency, which could be as soon as Thursday, August 22 according to the Zune Marketplace FAQ.
The Zune Marketplace's movie and television rental/purchasing functionalities will be taken over by the Xbox Video platform, whereas its musical feature set will become the domain of Xbox Music, provided you've got a subscription to the service that allows streaming to an Xbox 360. Microsoft recommends that you "spend your points balance prior to this change," but last we heard MS Points will be converted into an amount of local currency of equal or greater value.