The new run of Doctor Who seems like a pretty worthy successor to the series to date. The stories are variable in quality: some quite good episodes, some silly bughunts, but generally good scripts. The special effects are mediocre (including a few of the obligatory bug-eyed rubber suits), but it wouldn't be a BBC science fiction series otherwise.
The story really has three characters, who were the strength of the run. The protagonist really isn't the Doctor this time -- it's very much the Companion, Rose Tyler. Rose is a classic viewpoint character, and a bit of a Mary Sue: the 20ish girl from blue-collar London who gets swept up in the Doctor's wake. I'm sure that some will be turned off by that, but I liked her: she embodies a genuine sense of wonder that is appropriate for the situation, and is thoroughly encouraged by the Doctor.
The Doctor himself is a blast. Christopher Eccleston plays a Doctor entirely of extremes: grinning maniacally one second, deeply in funk the next. This is a Doctor who is really suffering on a psychic level. I didn't see the previous season, but the final Time War between the Timelords and Daleks lurks constantly in the background, and the Doctor is acutely aware of being the last of his race. Suffice it to say, the Daleks aren't quite dead, and the Doctor is torn between an absolutely visceral hatred of them, and a self-hatred for letting himself feel that way. The mania is laid over that, but it always feels a bit shallow, the feelings of a man who is deeply haunted and trying desperately to forget.
The third character, coming in towards the end of the run, is Captain Jack Harkness. He's a secondary character, but enough of a hoot to be worth calling out. He's sort of the midpoint between James "Tomcat" Kirk and Flashman, almost the avatar of Chaotic Good. He's a Time Agent gone rogue, and exemplifies the concept of the rake: a flamboyant scammer, trying to do well for himself but almost self-consciously heroic. He's just plain fun, and I hope he returns in future seasons. (It's also worth noting a sign of the times: he is quite casually bisexual, flirting with everyone around him. When marching off to apparent death, he gives both Rose *and* the Doctor a firm kiss.)
The chemistry between these three is the entire strength of the series, and it's strong. In particular, the relationship between the Doctor and Rose is complex and subtle: he's part mentor and part friend, with both father-figure and possible lover implications under the surface. (She spends practically the entire season telling people that he isn't her boyfriend.) After Jack appears, he's the third wheel and knows it, and you can sense just the tiniest regret about that -- but Jack never lets anything get under his skin too overtly. The bond between these folks comes quickly, but they pull it off well, getting a working relationship that many shows don't achieve for a couple of seasons.
The season is surprising for having a *theme* more than a story. The theme is "family", and it runs through everything happening here. Rose and the Doctor frequently return to modern-day London, and Rose's mother is a major character. The Doctor's sense of being alone in the world is palpable and often comes to the surface. The aliens they encounter tend to have family issues driving them; heck, even the Daleks get a family story (after a fashion)! It's rare to see a series focus a season on a theme rather than a simple plot, and a nice change, especially when they have a lot to say on that subject.
That said, there is an overarching plot: not so much a Babylon 5 style relentless freight train, so much as a large number of threads that gradually pull together. I do recommend watching the season from the beginning: while the various episodes can mostly be watched individually, the end of the season tends to refer back to the beginning.
I won't say that this is the best science fiction around -- there is an ambient cheesiness through much of it, and as I said the quality is variable. But overall I thought it was a strong season, well worth watching. I can only hope it continues to be similarly good next season; we shall see...