I was first introduced to The West Wing at university by my husband (he blogs about gaming and books at Citadel of Davegotsu).
The first time we watched the entire series it took us about nine months. The second time took us about three months, by that time we were working similar hours. It is unusual for us to spend so much time watching a non-SF series.
The series about a fictional US president, set mostly in the White House, ran from 1999 to 2006 and was created by Aaron Sorkin, who is a televisual maestro.
The West Wing was a great blend of drama and humour, an entertaining character-based series that was also about really important issues. The characters were engaging, the story lines were interesting, and the dialogue was regularly brilliant.
The plot lines could go from the lighthearted to the dramatic. Unsurprisingly there was a lot of content dealing with US politics, which managed to interesting even to a fairly unpolitical Brit like myself.
Aaron Sorkin is skilled at creating shows with characters and situations that you care about, even if you don't have a particular interest in the content. A good example of this is Sports Night, a program about a US sports show, something that an unsporty girl like me would normally never be interested in.
The characters and their interactions really made the show. The White House staff were shown to be extraordinary people -not only doing important and challenging jobs, but dealing with various personal problems in ways that only ever felt human and realistic.
I could list the great things about all the characters: Toby's dry sarcasm, Josh's determination, Charlie's loyalty, Leo's wisdom, CJ being one of the best female characters on television.
I think I'll stop myself there or else I'll go on all night.
President Bartlet was exactly the kind of president that many of us wanted America to have - he was smart and erudite, compassionate and liberal, and he really struggled with some of the serious issues he faced as President. He wasn't perfect, but he was likeable and you could respect him even if you didn't agree with all his choices.
One of the nice things about the series is that it is liked by many geeky types, but can also be recommended to people who aren't into SF.
I remember that the Sci-fi Society at my university had a Big Block of Cheese Day. The Chair (who was from Gloucestershire where they are very serious about cheese) brought in a block of cheese with a small US flag stuck in it. I can't remember if we asked any important questions, but I'm sure it was all done in the spirit of Andrew Jackson.
I would recommend the West Wing to anyone to who enjoys an intelligent TV drama.
Here's a link to the Wikiquotes page, it has great examples of the witty dialogue, but I must warn you it's pretty distracting.