Ooooh, Doctor Who, of which I am a long time fan. I was good to go in the years between the old and new TV show, with the two ongoing series of novels that continued his adventures.
Right now, a major favorite is Ecclestone. He accomplished a Doctor that was so edgy, intense and dangerous a Doctor, so very compelling; yet still clearly identifiable as the Doctor, while at the same time challenging old conventions of what we thought the Doctor was supposed to be.
I've gone back and forth so many times on companions, it's really hard to say. A couple from the novels are very interesting characters.
I can't think of a favorite villain off the top of my head, but here is a monster that probably doesn't get mentioned too much: I like the Fendahl. A gestalt creature, with 12 (Lovecraftian) sub-creature components, and a human/humanoid core. The product of an evolutionary cul-de-sac, from the original Fifth Planet of our solar system, it's feeds on death (it is death, how do you kill death itself?). It was so notorious it became a part of Time Lord mythology; the Time Lords were spooked enough by it that they time-looped the planet out of existence. This creature is one of the most fascinating concepts I love from the old show.
Another great enemy is from the novels, where the Doctor intersects with a Time War (of a different shape than we see in the TV show) where the Enemy of the Timelords is specifically not the Daleks, yet other than that remains a complete mystery (and is still a matter of speculation today). It's the mystery, the guessing game, that makes these unknown adversaries compelling.