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Note: Before we jump into discussing the Black Riders in The Two Towers, you might want to take a peek at the Black Riders' "Character Analysis" for The Fellowship of the Ring for some background.
You know those horrible, horseback-riding, shrieking ghost kings from the first book, the ones who stab Frodo in the shoulder and almost kill him with poison? Well, they're back for The Two Towers and now they're flying. Yep, the nine chief minions of Sauron are worse than ever. Since they are wraiths (another word for ghost) the Nine can't be killed by usual, physical means. When Glorfindel drowns them all in the first book, their horses go down, but the Nine themselves are fine—they just have to find new wheels, so to speak. And what they come up with is even worse than demon horses. Now, they're astride hideously terrible winged dragon things.
What with being able to fly everywhere, the Black Riders have gotten even better at spreading fear over Middle-earth. When one flies over the Dead Marshes, Gollum falls flat on his face and won't move for hours out of terror. And they keep coming back, always far away, always super-fast. They are not much of an immediate threat to Frodo or Sam, but their frequent movements remind us that Sauron is on the move, even if we don't see much of him in person. They are proof that this whole war business is actually getting underway.
They don't just build up suspense for Sauron's war, though. The Black Riders also remind us of what's at stake for Frodo and all of his friends personally in this Ring quest. After all, the Black Rider origin story is also a moral lesson for all Ring-bearers, even little hobbits. Think about what Faramir tells Frodo:
"It is said that their lords were men of Númenor who had fallen into dark wickedness; to them the Enemy had given rings of power, and he had devoured them: living ghosts they were become, terrible and evil. After his going they took Minas Ithil and dwelt there, and they filled it, and all the valley about, with decay. (4.6.103)
In other words, watch out. No matter how great a man you are, you run the risk of being ruined by ambition and arrogance if you carry Sauron's Rings of Power. And as the Bearer of the One Ring, Frodo has to work really hard not to turn into a wraith like these guys did, which, judging from their pathetic half-lives under the shade of Sauron, seems like a generally bad career option.
Of course, Faramir's warning also shows us how deeply awful Frodo's immediate future is going to be. Frodo has to climb past Minas Ithil (now Minas Morgul), a valley filled with "decay," in order to get into Mordor. And as he's walking, he'll be going straight past the home of the Ringwraiths, you know, the guys who stabbed him in Book One? The guys with the special senses for Ring-bearers? This does not sound like it's going to turn out well, that's all we're saying.