OK, if we're going to do ages-when-we-first-watched-Buffy, I beat all of you because I was in my 50s!
I think it was back in 2000 when my daughter (then in her middle 20s) suggested I watch a couple of episodes. I knew of the show, because my son (then in his early 20s) was a fan. I'd dismissed the show because, you know, cute blonde kicks ass, it's a teen show, etc.
The two episodes my daughter made encouraged me to watch were from season 4: "Hush" and "Restless". I won't say anything about those episodes in order to avoid spoiling them for new viewers. But those who recall those episodes will know why I looked like this ->
, but in a good way. (I then borrowed my son's DVDs to watch from the beginning, and then went on to watch every episode until the very end.)
For a TV show that was marketed as a "teen show", it's at times very deep, with much more adult/philosophical themes as the show developed. I think the first few seasons are ok for youngsters aged 11 or so, but the later seasons do get very dark at times (but are good for prompting discussions). When the show started on UK TV, it was shown in the 6 pm slot (because, you know, it's a teen show), but as the seasons went on and the show got darker, there was an edited version at 6 pm and an unedited version at 10 pm.
I liked Giles ? especially when at moments of stress he polished his glasses with his tie. I didn't care so much for Angel. Spike ? well, his appeal is timeless. And his coat. 