I agree with Rune about the Nazgul. Although they were scary and
real enemies, they were an actual threat only until Bruinen. They were much scarier with living horses than with beasts, living or undead. Horses are living creatures, with a will of their own, and one should be able to predict their behaviour at least a little bit. Thus, it makes me wonder how corrupted those poor animals must have been to carry the Black Riders. I even feel a little pity for them though I am no animal lover. The same cannot be said about the fell beasts. They are just beasts born to serve Sauron, unlike the horses we know. This makes them a little less scary creatures than horses, and it affects also to the Nazgul. They can be ever present without actually being seen. They don't have to be close to keep watch. And in my opinion, the closer they are, the scarier they are.
The most terrible moments I've ever had with Tolkien were the ones with the Balrog. Maybe it's understandable, since I was 11 when I read the Lotr for the first time, and it was the only time I was truly afraid of the Balrog. The movies hadn't come out yet, so I created a very own conception of the Balrog, and I must confess that my balrog has always been much scarier than the one shown us in the movies.
Sauron was scarier in The Silmarillion. In those days he was nothing but a servant, he took risks and fought himself. Now that he's the one commanding armies from his tower, he doesn't seem so strong anymore. Really, I can't imagine he'd win an Elven lord in a song contest anymore. Not without the help of a bunch of Orcs.
Was this thread about the number of nightmares, the scariest characters would be the Nazgul. I've happened to have several nightmares about the Ringwraiths living in our cellar and attacking me when I have nothing better than a flick knife to defend myself with. By now, I have managed to kill already three of them. Still six (or five) to go, but I beat Éowyn.
However, one thing I love in Tolkien's books is that there are no creatures that cannot be slain; nothing that is evil is invincible. They cannot conquer for ever.