Well, Black Zero was more than just that silver age villain. In the John Byrne reboot, the Black Zero was a Kryptonian terrorist organization like Al Queda; their supposed cause was the fight for clone civil rights (Krypton at the time using clones to harvest organs). The final act of the Black Zero was to fire a sustained nuclear beam into Krypton's core in order to destroy the planet, but an ancestor of Jor-el stopped the beam. Unfortunately, the damage was done, and this eventually led to Krypton's destruction.
The new Superman movie seems to feature Phantom Zone criminals, so it's not far fetched to believe that Supes will face members of the Black Zero who were exiled. In this continuity, we may even find that Zod is part of the Black Zero.