The short answer? All of it. I don't think there's one specific thing about it that draws me in...it's the whole Buffy package that makes me love it so much. But, since everyone's basically telling their life stories, I figured I might as well, too.
A little more than a year ago, I saw the first two seasons on iTunes, and, because I had heard good things about it and was pretty into supernatural, vampirey stuff, I decided to buy the first episode. I'll admit, while I was watching it, I thought, "Everyone is raving about this?" But as the episode progressed, I started to get into it, and after the cliffhanger at the end of WttHM, I had to get the second episode. The first season got better after each episode, and I started liking it because I just thought it was a lot of fun...oh, and because I was starting to get a huge fangirl crush on Angel (but, after a few episodes with Spike, I completely forgot about that.)
It wasn't until around the middle of season 2 that I really started getting into it. It started to develop a very interesting plot, the writing and acting became the best I'd seen in a TV show, and I was becoming very drawn to the characters. By the end of the season, it was my all-time favorite show, and that same mix of great acting, writing, characters, and storytelling continued throughout the rest of the series and kept me drawn in. In fact, it still keeps me hooked, even though I finished the show last year.