Buffy: I vaguely remember one of my close friends in primary school was very into Buffy. She talked about it, a lot, and eventually I ended up watching it. I fell in love with the show, and from there...Well, here I am? Strangely enough, she's no longer a fan. She did her job of getting me into the fandom. 😉
Angel: Mostly because I was a fan of Buffy, and I heard that Angel had his own spin-off show, I decided to give it a try, deciding before hand it 'wouldn't be as good as Buffy' and was pleasantly surprised with how much I liked it.
Firefly: I think it was for my thirteen birthday? I asked for the DVD boxset. I'd read topics here, and random things on google, about Firefly and decided I wanted to give it a shot, even though I wasn't sure if I liked the plotline, I just liked the fact it was a Joss show. I'm glad I saw both Firefly and Serenity, because I fell in love with them both, even though I didn't think I would. 😀
Dollhouse: It was hyped up a lot online before hand. I remember reading all kinds of things on here, Whedonesque, places like that. I ended up watching the first episode online after the US release date. Again, just because it was a Joss show.
To be honest, if I hadn't watched Buffy and become a Whedon fan, I don't think I'd have heard of, let alone watched, any of his other shows.