Sci-fi is a philosopher's genre: a lot of sci-fi stories are essentially ethical or metaphysical thought problems dressed up with robots or mutants or parallel universes. I like the way a sci-fi story will push some reality past its expected limits to explore the implications.
So I tried watching it, beginning with the 2005 reboot...and I couldn't get into it. I really, really wanted to like this charming Northerner and his adventures in space and time, but for the longest time I couldn't manage to get hooked in.
Okay, relax. I've gradually come around. But it wasn't an instant love affair.
I think part of my slow start stemmed from the show's visual style. The sometimes poor special effects are notorious, but it goes beyond that. In general, I think the writers allow the storytelling to ride a little too heavily on effects, bad or good, and especially on the visual impact of various weird creatures. I prefer it when the impact of a TV episode flows from the suspense and mystery and weird twists of a well-paced story more than from the fear and disgust and shock value of strange and unsettling images. Star Trek keeps all of these things well-balanced, I think, whereas Dr. Who leans a bit too much on the latter.
Also, philosophical and ethical reflection is not as front and center in Dr. Who as in a lot of sci-fi. It's there, and I'm seeing it more now that I'm two seasons in. But a lot of episodes follow some pretty well-know sci-fi tropes and plot devices: robots who want to kill us, robots who want to make us robots, and of course zombies. Lots and lots and LOTS of zombies. There's not all that much treading of new ground or asking of probing questions.
However, as I said, I've now settled in and I'm enjoying the show quite a lot. I think the real genius of the series lies in the characters rather than the plot, and especially (of course) the central one. The sci-fi trappings are actually kind of non-essential to what makes the show great. That's why some of the best episodes are the time travel ones, because they delve a little deeper into the characters by placing them in a different historical and cultural context.
Speaking of the Doctor: am I the only one in the universe who likes Christopher Eccleston's Doctor best? I'm not really qualified to have an opinion on this since I've so far only seen him and David Tennant. Well, I did go back and watch one episode of Classic Who from the 70s, but the Doctor was unconscious for most of the episode, so I really didn't learn much.
Anyway, Christopher Eccleston's Doctor just has more...substance to him that David Tennant's. His performance has so much more weight and nuance and charm and doesn't rely on yelling and slap-happy bluster. David Tennant is adorable and Scottish, but lacks a little in artistic maturity. Also, David Tennant's Doctor and Rose get way too gooey. What is with all this hand holding and incessant hugging? Harumph.
And then there's that smile, which somehow carries the weight of the Doctor's thousands of years of pain and loss. That's acting for you.
UPDATE: About David Tennant? I take it all back. Still love Christopher Eccleston...but David Tennant is a more than worthy successor.