There are many amazing heroes in Lord of the Rings, among them Aragorn, Frodo, Bilbo, Eomer, and, of course, the awesomeness that is FARAMIR. But heroes must fight against something, and there are some exceptionally good villains in LotR and The Hobbit.
Sauron's most powerful minions are probably the Ringwraiths (or Nazgul, or Black Riders): nine men (we think they're men, anyway – as Strider tells us, they're “neither living nor dead.”) who have been twisted into Sauron's service and given special powers. They were created especially to track down the nine Rings, and are one of Frodo's chief problems. Their leader, the Witch-king of Angmar, is cruel and powerful, and cannot be killed by any man. In one of the most amazing scenes in Return of the King (both movie and book), he attacks Theoden and kills him (or rather, causes his horse Snowmane to crush him), but is then slain by Eowyn with the help of Merry. None of the other Ringwraiths are given specific histories or names, but they all have great capacity for evil by themselves and are doubly dangerous (nine times as dangerous?) when they're together.
Saruman is one of the turned-to-the-dark-side kind of villain; he was originally the head of the Istari, a “White Wizard”, but at some point (it's never revealed exactly when or how) he becomes corrupted by Sauron and switches sides, while still remaining in a position of trust. This makes him one of the most dangerous forces in Middle-earth. When it is revealed where his allegiance truly lies, he is, of course, deposed, but he goes and takes refuge in Orthanc with his slimy assistant, Grima Wormtongue. In The Return of the King, his stronghold is attacked by Ents. In the movie, he is killed then; in the book, he survives and is reduced to a beggar, along with Wormtongue.
A bit on her history: she has an ancestor, Ungoliant, who appears in The Silmarillion, a just-as-huge arachnid who does Melkor's bidding, but later nearly kills him, showing just how powerful she is.
Also, Shelob's name is “She + lob,” lob being an old English word for spider. Thus, “she-spider.”
Other notable villains are Wormtongue (who is Saruman's pawn and does a lot to corrupt King Theoden's mind), Gollum/Smeagol (the “misunderstood” villain – every movie has one of these!), and the orcs (which are the evil minions Saruman basically made).