Please note, I'm reviewing the new series, seasons 1-6.
This show is wonderful in its flexibility. There is nothing that it can't cover, no emotions that it can't pull, no concept that it can't run with. The series is an adventure story, a character piece and so much more. The secondary characters constantly change, the setting and premise is radically different in each episode and even the main character goes through some radical changes from start to finish, but it retains that same heart and soul that keeps pulling me in.
The series is enormous, but there is not a single episode I could honestly say I dislike. Not even the infamous "Love and Monsters". I love these characters, I love following the adventures they have, and I love the insane sci-fi concepts. Doctor Who doesn't bother with technobabble. It just tosses random words around and that's our premise for the week. Sometimes I think the writers just pull a few words out of a hat, make a scenario about them, and then try and figure out what in Yog's name is going on. That is NOT a criticism.
Doctor Who is essentially a framing device for whatever story the writers want to tell, but it's so much more! It can be as big or small as it wants, but the world it's built and the characters it follows are just amazing. It manages to pull some of the most cringe-worthy cliches in the book, and makes them believable, heartwarming or hilarious as the story sees fit. The narrative quality ranges from masterful to sub-par, but it never stops being great.
While not everyone has a tolerance for everything this series throws at you, it's so broad, versatile and fun that it's accessible to just about anyone. Anyone who has even the slightest interest in science fiction or adventure should give it a shot.