Anyone who watches Doctor Who only thinks of two things when you say “villain”: The Master and the Daleks. These are by far the two biggest enemies in the show. And to me, the Master beats of the Daleks by miles. He’s charismatic, he’s funny, he’s a genius, and he has a history with the Doctor. Oh, and he’s batshit insane.
While I do love many of the show’s antagonists, reoccurring or not, they just don’t compare. I loved the Carrionite Witches from the Shakespeare Code, and many other favorites come to mind too. The Beast, Lady Cassandra, and the Family of Blood are the first ones I can think of.
The Master is by far the best though. His sheer brilliance balanced with irrefutable craziness makes him a great adversary. The Doctor looks at him and knows that this is what he would be if he weren’t such a fundamentally good person. One slip up - kill one person who could have lived, neglect saving one person’s life when he could have - and that spiral of carelessness could turn him into the monster that the Master is. The Doctor knows this, thus knowing that the Master could be a good man. He tries desperately to save him, to let him redeem himself, only to have his help shot down at every turn.
Watching a childhood relationship crumble due to blind insanity and unwillingness to accept help is tragic, and makes for some great episodes. That’s why he’s my favorite.