It depends if we're talking about just the movies, the expanded universe into games and such (BFME, BFME II, and BFME II: RotWK), and/or the books. My favorite is a close call between the Witch-King and Sauron. Sauron I have a lot of affection for because of his accomplishments, ideology, and goals. Morgoth may have been more powerful, but Sauron was arguably the more intelligent, having brought about the downfall of the land of Numenor and rather than seek to destroy all life as his deposed master, desiring instead to dominate it. The most notable exploits of Sauron need not be elaborated upon. I think everyone is familiar enough with his infamous deeds in the Second and Third Ages.
The Morgul Lord ties the Dark Lord for me because he was not a simple servant like the other countless thralls that swelled the ranks of Mordor. He operated an agenda even after Sauron's downfall. The Witch-King founded the realm of Angmar and his stronghold of Carn Dum, captured Arthedain and Fornost, gave rise to the Barrow Wights, destroyed the tower of Amon Sul at Weathertop, overthrew Minas Ithil and christened it Minas Morgul, and lastly and my personal favorite, ended the line of kings. I always felt the death of Earnur was both very dramatic and tragic; you could picture the heroic ride of Earnur who finally accepts the Witch-King's challenge to engage him in single combat. Initially he refuses (under advisement by the steward) but seven years later when the Witch-King renews his challenge, he rides out to meet him with a brave company of knights, with neither the knights nor their king ever being seen again. Brilliantly crafted tale and it fleshes out the Witch-King better to know his exploits. You appreciate exactly what his presence means to the men of Gondor on the field of battle in RotK when you understand how the Witch-King has besieged the World of Men in the past.
In terms of heroes? Easily Theoden and Gandalf. As much as I love villains, these are heroes even a villain can respect and even admire. Boundless heroism and devotion fueling both individuals. Gandalf is a master strategist on par with the Dark Lord. He crafted the entire defense against Mordor in the Third Age, and without him no capable resistance would ever have been marshaled against evil. Theoden is such a staggeringly tragic figure who, even after all he has suffered, still refuses to acquiesce to the foes that assail him, ever rallying to bolster the spirits of his people, and selflessly plunge himself into combat if it means he can save even a single life; a true leader, and a hero if ever there was one. He lost his son, unknowingly cast out his nephew, and spent far too many days under illusory dotage when a lion paced restlessly within its imposed cage.
Just my favorites among the heroes and villains, though it's hard not to love Boromir & Faramir, Eomer, and Aragorn, Legolas, & Gimli.