Can Ringwraiths turn on their master?

[Legate of Amon Lanc]

I would basically second what Inzil said. Except for one thing. At one point, when the Nazgul come to the gates of Isengard in search for "Shire", Saruman says:

Originally Posted by Unfinished Tales, The Hunt for the Ring

"I know what you seek, though you do not name it. I have it not, as surely its servants perceive without telling; for if I had it, then you would bow before me and call me Lord."

Curious, of course. Saruman seems to imply that the Nazgul would obey him had he been the master of the Ring. Note please that it means really being the Master of it, i.e. being capable of fully using the Ring's power, I assume. So some sort of random Baggins could not do that, but somebody as powerful as Saruman possibly could. I also think that in some drafts or notes Tolkien explains that the Nazgul were afraid actually even of Frodo partially because of this (but mostly because they didn't know what he was capable of), but he implies that eventually, even if they sort of played the roles of servants, he would be unable to control them anymore and their will would prevail over his.

That said, Saruman could be, of course, completely off here. It should be considered that he was the most familiar with Ring-lore in all Middle-Earth at that time apart from Sauron himself, but then again, even the wisest can make a mistake (and especially Saruman was sort of known for this). In any case, we never had the chance to see the experiment at work. However, when it comes to the actual question if the Ringwraith would turn against Sauron, it will likely need a really strong "Other Ringlord" behind them. I could imagine possibly Gandalf with the Ring being able to turn the Ringwraith against Sauron, but still there will probably be a huge battle of will and anyway, the attempt would be so risky that even if somebody controlled Ringwraith with the One, I believe he would rather try to keep them as far from Mordor as possible, in order to diminish Sauron's influence over them.

Apart from this, the Ringwraith turning against their master is a totally impossible idea. Once they became enslaved by the Nine, it was over for them. At most, they could be made to obey a different lord wielding the One, as outlined above, but that's it.

[Inziladun]

Originally Posted by Legate of Amon Lanc

Curious, of course. Saruman seems to imply that the Nazgul would obey him had he been the master of the Ring. Note please that it means really being the Master of it, i.e. being capable of fully using the Ring's power, I assume. So some sort of random Baggins could not do that, but somebody as powerful as Saruman possibly could. I also think that in some drafts or notes Tolkien explains that the Nazgul were afraid actually even of Frodo partially because of this (but mostly because they didn't know what he was capable of), but he implies that eventually, even if they sort of played the roles of servants, he would be unable to control them anymore and their will would prevail over his.

I think you're referring to Letter 246. It seems to indicate that in order to be the true master of the Ring, Frodo would have needed not only to have taken possession of it, but also to have defeated Sauron in a one-on-one confrontation. It says the Nazgûl would have obeyed, or pretended to obey any commands of Frodo's that did not conflict with their mission (to distract Frodo until Sauron himself came to take the Ring). If Frodo had been able to keep the Ring from Sauron in that circumstance, he would indeed become Master, of the Ring and the wraiths under it. Frodo, of course, was not strong enough to do that. Gandalf, and the Keepers of the Three might have been. Saruman? Who knows, but my feeling would be negative. Saruman was dominated in a test of wills through the Palantíri, and it is said in the books that Sauron was greater. So I think the result if he had tried to keep the Ring from Sauron would have been the same as with Frodo, ultimately.
As for what being "master" of the Ring entailed, I would say it gave one full control over every thing that had been wrought by the Ring, including the Nazgûl.