This is a hotly debated issue. Some believe that the Nazgûl kept their own rings and were enslaved and controlled by Sauron through their rings. This side also believes that the Nazgûl derived their power as Ringwraiths by wearing their own rings. The only clear statement for this stand is during the Council of Elrond where Gandalf states that "The Nine the Nazgûl keep." There are faults with this position;

1. Why was there no ring left on the ground after the Witch-king was defeated by Eowyn and Merry, whereas Sauron's Ring was left for the taking by Isildur when defeated by Gil-galad and Elendil?
2. Why didn't Frodo, as Ring Bearer, see the rings on the Ringwraiths on Weathertop and at the Ford of Bruinen when he saw their swords, pale faces, their eyes, and their crowns?

Most of the evidence points to the opinion that Sauron himself held the rings. In the Fellowship of the Ring, Gandalf explains the history of the Rings to Frodo and tells him that:

"So it is now; the Nine he had gathered to himself; the Seven also, or else they are destroyed. The Three are hidden still." [The Fellowship of the Ring]

This statement is clearly in context with rings and not wills as mention of the Seven is made. We know of no wraiths or slaves that wear the remaining Seven. Therefore, gathering the Nine and Seven to himself means just that - Sauron has the Nine and remaining Seven Rings in his physical possession.

Galadriel also confirms this by telling Frodo while in Lothlórien:

"You saw the Eye of him that holds the Seven and the Nine." [The Fellowship of the Ring]

Then we have the following accounts from The Hunt for the Ring in Unfinished Tales:

"At length he (Sauron) resolved that no others would serve him in this case but his mightiest servants, the Ringwraiths, who had no will but his own, being utterly subservient to the ring that had enslaved him, which Sauron held."
"They were by far the most powerful of his servants, and the most suitable for such a mission, since they were entirely enslaved to their Nine Rings, which he now himself held..." [Unfinished Tales]

These statements clearly show that it was Sauron who held the rings and so controlled the Nazgûl.

The most definitive statement comes from one of his letters describing the situation of Frodo at the Cracks of Doom and is extremely informative concerning the nature of One Ring:

"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..." [The Letters of J.R.R. Tolkien #246]

It would appear from the above body of evidence that when Sauron first claimed the Nine he then gave the Nine Rings to Mortal Men who used the power of their rings for dominance and control. In the end, they faded and became Wraiths - at which point Sauron took their rings back to hold and so control his most feared servants.