The fact that Joss Whedon had the presence of mind to finish it after seven seasons means it's finite. It never became one of those shows that went on for ten seasons, and ultimately the interest wanes and so therefore it's a bit sad by the time you get to the end. It drives right the way through without a let-up - and consequently people still like watching the show.
Things like The X-Files were brilliant, and then they just sort of petered out. The thing that's great about Buffy is that the writing was consistently good all the way through. Yeah, there were one or two episodes [that weren't so great], but there were some outstanding episodesAnd this got me to thinking: how does this apply given that Joss has blessed the comic series "Buffy Season 8", then season 9 and now season 10, as continuations of the story and has said they are in the official BuffyVerse?
So I don't know that Buffy can be considered "finite" since the series has continued, but only in a new medium.
But, what do you think? Comment below.