I like it quite a lot, though it does have some rather glaring flaws to get past. The primary one is the utter ugliness of its look. The show began in the 60's and still looks as if it were filmed in the 60's. The special effects are AWFUL. The villains generally look dumb, with especial mention for THE villain - the Daleks. Flying trashcans with evil plungers are ... stupid. Almost everything is filmed on set, and it looks it. It's just not an attractively filmed show.
What generally rescues the show is the acting by the leads and the fact that the show likes to have fun - it doesn't take itself seriously. Rose is adorable and I love Eccleston as the Doctor - I'm really going to miss him. The show does a good job with continuity - which is no joke when time travel is involved. The emotional journeys add a needed weight to a show which is otherwise rather silly.
Rose - I really liked this episode as an introduction to the characters. The plot ... was kind of dumb. But it was fun enough that I didn't mind for the most part. (Although my suspension of disbelief really really got a workout when Rose didn't notice that Mickey had been replaced by plastic.) And ... poor Mickey. Rose really didn't give a second thought to abandoning him.
The End of the World - I liked seeing Rose deal with the new world she launched herself into. Cassandra was over the top as a mustache-twirling villain.
The Unquiet Dead - I enjoyed this episode the most of the early ones, I think. It was a little creepy and had a nice campy feel. The supporting characters worked fairly well, especially Gwyneth.
Aliens of London, World War Three - OW. Except for the fallout of Rose vanishing for a year, these episodes were DREADFUL. The Slytheens sucked as villains. And ... note to the film-makers - if your effects suck, do not spend so much time showing the same thing (the Slytheens unzipping themselves) over and over again.
Dalek - You know, Eccleston really really tried to make the Dalek seem scary. He acted his heart out. But at the end of the day, I just could not get over the Dalek being a flying trashcan. I cracked up every time someone was scared of it, which is not the intended effect, I'm sure. Von Stattan, or whatever his name was, was an annoying stereotype. I think that with better production values and general execution, this episode could have been good, but as it was, eh.
The Long Game - Adam is quite the idiot, isn't he? I'm glad they got rid of him. This episode was ok. I didn't have much of a reaction to it.
Father's Day - Despite the silly monsters, I really enjoyed this episode for the emotions in it. Much like Farscape, Dr. Who is best when it focuses on its leads emotional journeys. This kind of episode is sort of mandatory for a show that relies on time travel, but it was well done for the most part. I normally worry about time travel consistency and the like, but this show does a remarkable job of letting me not think about it too much.
The Empty Child, The Doctor Dance - Now these are probably my favorite episodes in the first season. I love the creepiness and the way things came together in the end. Nancy was fantastic. Captain Jack is kind of an ass, but entertaining none the less. I wasn't a fan of Rose flirting with him, however (I might be a little 'shippy with her and the Doctor). And the happy tag (for once) was just wonderful. It was earned.
Boom Town - Considering this episode involved the return of my least favorite villain, I enjoyed it much more than I expected. It was surprisingly slow, all things considered. And once again, ow for Mickey. Rose's obliviousness where he's concerned is difficult to take. Either cut the boy loose or come back to him. You can't go running around the galaxy and expect him to wait for you.
Bad Wolf, The Parting of Ways - The Daleks again? Oy. The Bad Wolf resolution was less satisfying than I'd hoped. I did enjoy Rose coming back to save everyone - and the Doctor (in a way). The explicit reality show updates were kind of absurd. They felt played out - maybe because I've a) seen Death Race 2000 (the original) and b) hate pretty much all "reality" TV.
I have not seen anything past Season 1 (except for "The Girl in the Fireplace" and "Blink") - so no spoiling me.