Why did the Nazgul not succeed in Bree and on Weathertop?

[The Squatter of Amon Rûdh]

I think it's worth quoting the above passage in full, since it reveals a lot about the innate powers of the Ringwraiths.

Originally Posted by J.R.R. Tolkien (Letters #210)

Their peril is almost entirely due to the unreasoning fear which they inspire (like ghosts). They have no great physical power against the fearless; but what they have, and the fear that they inspire, is enormously increased in darkness. The Witch-king, their leader, is more powerful in all ways than the others; but he must not yet be raised to the stature of Vol. III. There, put in command by Sauron, he is given an added demonic force. But even in the Battle of the Pelennor, the darkness had only just broken.

Therefore, Frodo's call to Elbereth and attack on his assailant succeed because he overcomes his fear, which is the Ringwraiths' chief weapon. Perhaps Cardinal Ximenez could be defeated in the same way, but that's another argument. Of course, knowing that Frodo had received a Morgul wound, which was enough to kill the great Ruling Steward Boromir (not to be confused with his namesake from the Fellowship), probably played a part as well. What would be the point of risking a fight with Aragorn (in which one or more of the Nazgul might themselves be destroyed, just as the Witch-King was by Eowyn) when the Ringbearer will soon become a lesser wraith himself? The Nazgul aren't really that powerful: they seem so only because of the fear they inspire. This, of course, makes more sense when one considers Sauron himself. He deals in treachery and betrayal, and those are things which he expects from his followers. Why would he want minions who were powerful enough to offer him resistance if the thought took them?

The presence of Aragorn at Weathertop and Glorfindel at the Ford of Bruinen, together with the surprise release of the floodwaters, are unexpected setbacks to the Nazgul. Sauron knows enough to know that hobbits are small and unwarlike, so his Ringwraiths ought to be enough to overcome four of them. It's only the presence of those factors that cause their efforts to fail so early in the story, even if one takes into account the hidden qualities of the hobbits themselves. It's a wonderful irony that those whose main weapon is fear are themselves so easily overcome by it.