"Seize the moment...'cause tomorrow you might be dead." Buffy, Episode 1 "Welcome to the Hell Mouth."
I'm a big fan of Whedon's work, starting with his writing on "Roseanne." And let's not forget "Toy Story." I think "Buffy" was something of a milestone for television. Season 1-5 were brilliant, much of season 6 was great. The show really faded away with the last. But what came before it was brilliant. I came to the show fairly late and really only watched it in its entirety once the DVDs came out. (I have the box set of the complete series now.) And what really took me by surprise was that the show used demon-hunting as a starting point for exploration of teen angst and growing up. But Whedon took his teens' problems seriously, so while so much of it was reverential and humorous, it was always true to life. There was so much for teens and young adults to relate to, even if our high schools were not literally sitting on top of the Hell Mouth. And the most impressive thing about Whedon's work (this is also true of "Angel") is just how much we got to see the characters grow. Every single character is completely transformed by the time the show reached its end, and transformed convincingly.
I do think that in some ways "Angel" was an even better show than "Buffy." If "Buffy" was about growing up without falling off a cliff, "Angel" was about grown-ups trying to climb out of a hole they fell into. Perhaps I just personally related to that more because I was no longer a teen by the time I started watching the shows. But "Buffy" provides a great deal of rewards for people of all ages. It's some of the best writing on television ever, and the mythology Whedon and co. developed over the course of 7 years (plus 5 of "Angel") is so huge and so complex and really stunning. It was fascinating watching some characters make appearances on both shows and telling the same stories from different perspectives (Angel, Darla, Druscilla, and Spike's time in China during the Boxer Rebellion - when Spike killed his first Slayer - is just one example. That story was told once on "Buffy" and then re-told by a different character years later on "Angel" - revealing details that redefined everything.) Such attention to detail by the writers was really staggering, and the shows were full of them.
Some of my favorite episodes on "Buffy" include, of course, "Innocence" - when Buffy slept with Angel and he lost his soul. "The Body" - when Buffy's mom died - was a small masterpiece. "Hush" - the almost completely silent episode with the ghoulish demons who stole everyone's voices - was brilliant, and the only episode of the series to get an Emmy nomination, for writing. (An interesting nomination for an episode with virtually no dialogue.) "Once More With Feeling" - the musical - is a classic. And I forget the name of the episode, but the one where Anya - still a demon - creates an alternate reality where Willow is a leather vampire chick (and a lesbian, years before the real Willow came out of the closet), was great stuff. This is only the tip of the iceberg.
As far as favorite lines - there were at least 5 classics in every episode. Is there a book with great Buffy lines? If there isn't, there should be. The first thing that comes to mind came in one of the first episodes: when Buffy really wanted to go out on a date and Giles kept insisting she go patrolling instead: "If the apocalypse comes, beep me," Buffy says handing him a beeper.
"Firefly," unfortunately, didn't have a chance to grow. Fox sabotaged it. They aired it on Friday nights, out of order. And then they pre-empted several episodes for baseball, so it was sometimes 3 weeks before another episode aired. Once they said they'd air a new episode on Sunday at 1pm. When I tuned in at 1pm, the show was half-way finished. They actually started it at 12:30. How could any series survive that? It's a shame because the show had enormous potential.