At least twice in LoTR:FotR, ringwraiths cower away from bodies of water. The second time (the ford of Bruinen) can be explained away by their fear of some Elvish magical trap through the enchantment of the water; but what about the first time, at the ferry? One of the Nazgul could have easily made the jump onto the barge and quickly dispatched those pesky Hobitsses.
A note in The Hunt for the Ring, in Unfinished Tales explains:
This is the citation referred to in Royal Canadian Bandit's answer.
So your answer is that in-universe there was never an explanation given, whereas out-of-universe it's just a plot device.
It is common in folklore for evil or "unnatural" creatures to be unable to cross running water. For example, this is a traditional attribute of vampires: http://en.wikipedia.org/wiki/Vampire
Tolkien himself noted that this idea was difficult to sustain for the Ringwraiths. In particular, they would have had to cross the river Greyflood (which had no bridge or ferry) in order to travel from Mordor to the Shire. (I don't have the citation to hand, it may have been in Unfinished Tales.) He seems to have gone ahead with it anyway, in order to emphasise that the Ringwraiths were inhuman, undead creatures.
Ulmo = "He Who Pours" (a.k.a Lord of Waters) controls even underground waters in Arda. Ulmo, second most powerful of the Valar, totally opposed Melkor's (and thus Sauron's) program of dominating the Creation.
The Ring Wraiths are as anti-creation as you can get. To cross into (as opposed to over) Ulmo's domain would unmake the Nine (cf. the crossing of the Greyflood and their loss of form in LotR).
The Nine kings were given nine rings by Sauron. These rings modified them into the creatures that they became, creatures of darkness and evil. Their form or bodies perished and they had to wear armor and cloaks in order to be visible to others.
Wraith means ghost, spirit or something out of shadow, shadowy.
Since they cannot die, for they are not among living I will say that they can be "perished" or "ended", and use these word in this answer.
The Nine fear light, fire and water. They fear two of the key earthly elements of this world. They fear light and reside in shadow and cannot show a true form in this world. Hence the armor and cloaks which they wear. If we say they are the creatures of the darkness, than that statement would be true; but if we say they fear water because they are creature of the darkness, than that would be false for they also fear fire (we can associate fire with both good and bad). In the end some of them were "ended" by fire.
At this point, we can also speculate that they also fear the elements earth and air. Let me further explain this:
In LOTR we see that they fear forms of hot, cold and wet - from the above we can deduce that they also fear the dry form. They can only be "perished" by fire, or enhanced weapons (any of the above), but we can speculate that they can be "perished" by any of the above in an enhanced form. In truth, they fear all the elements of this world for they are the creatures of the shadow (the Wraith).
Furthermore there is another theory in which each of the elements have three properties, so we can provide a connection to the LOTRs "perishing" of the nine. Fire is sharp, subtle, and mobile while its opposite, earth, is blunt, dense, and immobile.
They can be "perished" or "ended" by fire. Which is Sharp, Subtle, Mobile, we can also find one of fire's properties in water Mobile.
So, in theory and as a connection to LOTR. Three of these properites need to be present in order to "perished" or "ended" a wright. We could see that in LOTR, but one or two of these properties can potentially harm it. Two of them seen in air and one of them in water.
From this we can deduce that they cannot be "perished" or "ended" by water but they can be harmed by it.
Additionally, the Nine cannot see like men do and don't like to walk and hunt in daylight, but at night in shadow.
Crossing the river for them was a nuisance.
They crossed the river in fear, anger and disgust, but they knew that it wouldn't kill them in the end. It would mean the end to their horses (enhanced by evil, but still horses of this world) and their hunt, but not them. They knew they could lose this battle if they crossed it, but it was all that they could do at that point in time, for they are drawn to the One Ring like nothing else in this and their world (the world of shadow). In truth, they had to cross the river, they had no choice, for Sauron, and for the One Ring.
After this, the Nine received improved new mounts that wouldn't stop them at rivers, the Fell beasts.
This aura also protects them from the properties in elements, which I have talked about above in this answer. Their aura can poison water and pollute the air around them. Leaving them unharmed and protected.
They were physically weaker in the LOTR - Fellowship of the Ring, as also their aura was weaker. We could see that from the crossing of the water and small portions of fire when Aragorn drove them away with two burning sticks.
Situation which you are referring to with the ferry, only happened in the movie and not the book. For in the book the Nazgul arrive later and find that there are no more boats left for them to cross the river on.
It is very plausible that it is a holdover of the power of Ulmo. See this forum thread for more...
Before my answer, I think it is important to remember that this is a work of literature by Mr. Tolkien (revered writer, who used his writing as an expression of his philological passion, and in an effort to backwards extrapolate the English language, and to create a mythology that was unique to England, based on "explaining" folklore and cross-cultural mythology around a central (and fictional) theme...it is not a scientific treatise on Unified Field Theory.
That said, the powers of the Valar have always remained very undefined. As an example, Osse anchored Tol Eressea to the Ocean bed with seawead, but Ulmo (his superior) could not uproot it. The Valar have been given (literately) nearly unlimited power at times, and very diminished powers at other times, so all of it is deus-ex-machina (including the "once-flat-world" premise). This needs to be viewed as a work of (amazing) artistic fantasy, not a work of scientific fact.
Having said this, water has a connotation of purity - all was pure before "Arda marred", but it is the nature of water to remain unspoiled, even in the face of Morgoth's Ring. Of all compounds of earth, water is the simplest, the most pure, the most basic to life. It equates with the goodness of nature, literarely. The ringwraiths, by contrast, represent that which is unnatural (wraith = writhe = anglo saxon word for 'twisted' or 'bent').
The role of the Valar in the 3rd age is not made clear...they did send the istari much earlier, but in a supporting role, and most of the Valar had stopped taking direct intervention into the affairs of Middle Earth (especially in the Age of Men, whom the Valar have never tried to influence, and when they have, it has rarely been for good - please don't ask me for citation, 'the lost road and other writings', i think).
Whether through direct intervention or not, Ulmo "came rarely to Valinor" and has always been more concerned, compassionate, and active than most of the other Valar. When asked, Tolkien didn't mention this in his letters....why? who knows? It's an obvious answer. Maybe his car broke down that day and it slipped his mind...what some of us consider cannon, he considered a book. What he did say (or create the idea of) is that the Valar put into the world (through their music) what measure of strength and quality they posessed - by this, I mean that Ulmo's spirit flowed through the water, and gave it its goodness, whether he was directly intervening or not. Just as Melkor (most powerful of the Valar) put his spirit into marring Arda (making the world an imperfect embodiment of his malice, but in doing so, weakening himself), so also did Ulmo give to water (and Manwe to air, and Aule to the bones of the earth, and Sauron to the 20 rings).
Point being that the purity of Ulmo (who most of all has always contested evil) ran through rivers. It is not said that the Nazgul died when they touched water, only that they feared it...because the sensed Ulmo's presence and it's purity - much like a man with vertigo does not die when he climbs a ladder, but he will avoid one. Perhaps their conversion to spirit (fea) from body heightened this, much as an elf (aware of the distinction between fea and body) is more attuned to it (as discussed between felagund and an old human shaman woman on the nature of spirituality, elves, and humans...again, i forget the title to cite it).
To summarize, I believe the ringwraiths has a strong hydrophobia because their primarily spiritual makeup sensed Ulmo's purity and feared it.
Let's be honest, after Melko and Manwe, Ulmo was the third most powerful being there ever was under Iluvatar. By comparison, the witch-king was a mortal man (albeit powerful and enhanced by his ring, but human, and his ring was one of 20, made by sauron, who is, by far, Ulmo's inferior)...do the math...a portion of Sauron's strength vs a portion of Ulmo's strength = a man afraid of crossing water.
I welcome supporting or dissenting opinions.