The One Ring gave Sauron control of the Nine, yet when it was taken from him he still possessed the power to control them (or, at least he regained it towards the end of the third age). Why is this? The Wikipedia article mentions that he drew the Nine to him, but not how.
After the wearers of the Nine Rings had become the Ringwraiths, Sauron -- who at that time still possessed the One Ring -- took their Rings from them. In a letter, Professor Tolkien wrote,
Sauron ... still through their nine rings (which he held) had primary control of their wills.
from The Letters of J. R. R. Tolkien; emphasis mine.
Despite no longer being in control of the One Ring, Sauron still maintained control over the Nazgûl through each of the Nine rings which he regained while still in control of the One.
Letter #246 explains that even if someone else had control over the One Ring, the Nazgûl would still ultimately obey Sauron:
Sauron sent at once the Ringwraiths. They were naturally fully instructed, and in no way deceived as to the real lordship of the Ring...But the situation was now different to that under Weathertop, where Frodo acted merely in fear and wished only to use (in vain) the Ring's subsidiary power of conferring invisibility. He had grown since then. Would they have been immune from its power if he claimed it as an instrument of command and domination? Not wholly. I do not think they could have attacked him with violence, nor laid hold upon him or taken him captive; they would have obeyed or feigned to obey any minor command of his that did not interfere with their errand - laid upon them by Sauron, who still through their nine rings (which he held) had primary control of their wills..