Gilmore Girls ran from 2000 to 2007 (7 Seasons) on the WB and now can be found either on DVD or on Sidereel: http://www.sidereel.com/Gilmore_Girls
The show centers on the characters of single mother Lorelai Gilmore and her daughter Rory Gilmore and takes Rory from her first year of high school to past college. Lorelai had Rory when she was 16 and the two have an extremely close relationship, usually acting more like friends than parent/child and usually going back and forth between who is the more responsible one as a lot of the time Rory is in fact the one taking care of Lorelai. One of the distinguishing features of the show as a whole is that all of the characters talk extremely fast and spout a large number of references to other things (mostly pop culture). According to IMDB, the script for one episode of Gilmore Girls is roughly twice as many pages as a normal hour long show because of the amount of dialogue.
As written in wikipedia, "The series explores issues of family, friendship and romance, as well as generational divides and social class. Ambition, education and work also form part of the series' central concerns, telling Lorelai's story from pregnant teen runaway and high school dropout to co-owner and manager of the Dragonfly Inn. Rory's transition from public school to the prestigious preparatory school, Chilton, is similarly followed by the series, exploring her ambition to study at an Ivy League college and to become a foreign correspondent. The show's social commentary manifests most clearly in Lorelai's difficult relationship with her wealthy upper-class parents, Emily and Richard Gilmore, and in the interactions between the students at Chilton, and later, Yale University."
I'm not entirely sure what demographic the producers of the show were intending for their audience, but I believe viewers young and old enjoy the show. According to wikipedia throughout the first 4 seasons of the show it came in first with women 18-25 and it also has won numerous family show awards.
I think the show has a lot of appeal to different ages because of the types of issues that Gilmore Girls explores as stated above. It is clearly a show for entertainment but I think there are still things to be learned and educational possibilities that come from the show. One of which, is definitely the importance of family and being there for the people you care about. You even find that idea in the opening credits with the theme song: http://www.youtube.com/watch?v=bhIRywAOjZ0
The two main characters have a unique relationship, which I think a lot of people probably wish they could have with their parents. And while the two lead women have their fights, in the end they really do need and love each other. There is also definitely a running commentary about social class and socioeconomic status throughout the show. Lorelai's parents are in the wealthy elite and when she becomes pregnant, Lorelai (at least in her parents eyes) brings shame to her family and to their reputation. Instead of sitting back and accepting what her parents deem to be appropriate (namely marrying Rory's father and staying quietly at home) she longs for adventure and so takes off on her own effectively estranging herself from them until the time that she realizes she can't afford to send Rory to her dream school and so asks them for help. Throughout the series there are a lot of conflicts that arise in the form of money and status which is an interesting topic that not tons of shows often explore.
Gilmore Girls uses a mixture of drama and comedy to explore deeper issues, but at the heart it is never an "educational show" which, I think, is one of the reasons it is so popular, even now after it has been off of the air for 3+ years.
