What a great idea for a thread!
I, too, caught on to Buffy late, but now it’s my favorite show ev-ar. In fact, to me there’s just nothing that could ever compare. The shows here (many of which I’ve seen and enjoyed, and the ones I haven’t, I’ll be checking out immediately) are good, but for me nothing will ever live up to Buffy. That’s just how it is. 
Anyway, for other good shows, I’d enthusiastically second (third, whatever) Scrubs and especially Veronica Mars.
Veronica Mars is like Buffy crossed with Alias (which I also like, but agree with Peter that it definitely went downhill after the first two seasons) - it’s got a very strong, likeable female lead, who just happens to be an ex-popular blond teenager, her wacky friends, and her great relationship with her single parent (a father, in this case). The gimmick is that her dad is a private investigator, and she helps him out with his cases, and takes on cases of her own at high school. Plus Veronica’s best friend was killed (before the show started) and there’s an overarching plot thread about who killed her. Kind of Harriet-the-Spy meets Twin Peaks. Or something. Some of the lines seem very Buffy-esque to me, such as this exchange between a student at Neptune High and the principal:
Principal: I’d like a word, Logan.
Logan (without missing a beat): “Anthropomorphic.” It’s all yours, big guy.
Principal: [looks bewildered]
That one had me rolling. Just, to me, struck that Buffy note that I’d been missing. Anyway, that show’s a bit uneven, still finding its feet, but I have very high hopes for it. (Of course, since it’s a quality show, that means it’s doomed for sure.) I’d highly recommend checking it out.