A goal. Being evil in general, or simply killing to eat will get old fast. The goal could be as simple as trying to hurt or kill Buffy, but it has to be something. As awesome as Angelus at the killing, he would have gotten boring quickly if he hadn't had breaking down Buffy and then ending the world as his goal. The exception to this rule would be if the villain is three dimensional and/or has a lot of character development, like Faith & Spike got.
Motive. They have to have a reason for their goal/behaviour, to make them more relatable. For example, creatures of non-human species could get away with acting non-human simply because they aren't human, while humans should have some sort of reason for being evil. Faith believed it was either use or be used, and she obviously had had issues in her past, making her a murderer. Warren seems to be a phsycopath (not sure if that's the right term). It seems like he's been pushed around during his childhood, so that's one of the reasons he identifies with comic book villains who are also outcasts, outsiders who are disliked. But unlike them, he didn't have power. So he made sure to get some. And that feels believeable to me, a former victim of bullies.
Something we can't explain. I want villains that feels believeable in the sense that I can somehow understand what they're doing, as mentioned above, but at the same time, there has to be something about them that makes me want to discuss their behaviour, to figure them out. If a villain's simply out for food, or wants to hurt others because he/she himself has been hurt, that could get old after a few episodes. There needs to be some sort of mystery. That's why I'm still find vampires interesting, even after seeing so many and getting that they kill for food and fun, things the more animalistic side of me can understand. Because I still don't quite get them. I don't get what a lack of a soul does, why some are more sadictic than others, or why some seem to be so similar to how they were as humans, while still being so evil. It's a mystery.
Of course, if they're too big a mystery, and lack of motive seems to me a big fat questionmark, that could be a problem.
Better than the last villain. A random kind-of-interesting villain will do for the stand alones episodes or the smaller arcs, but a Big Bad needs to somehow be more interesting than the last one.
No-no on the clichés. Fun for the random stand alone episode/issue, but not for a Big Bad. Which is why I yawn at The First wanting to end the world (only interesting in the first season 7 re-watch) and Angel's "I wanna make the world a better place for me to live in and, and oh, you're going to be my queen."-thing of Season 8. It's not as unique as the other Big Bad's we've seen, and I think that's partly why I don't like the seasons as much as I could have (okay, Season 8 has a lot of reasons for being not so brilliant to me, and that might even change when I continue to read).
New Big Bads, not old ones. This goes for smaller villains as well. Brining Amy back for season 8 worked, since we didn't see her a lot of on the show, but not Warren, who had a good run in season 5-6 and is only used for comedial relief now. i'm also very unhappy The Master was brought back in season 8. He was great in season 1, but didn't seem to have much to give in season 8, he became a joke, which I didn't like, since I liked recalling how scary he had been, back in season 1.
So I guess I want something like what I described above. It seems like Simone could be the or a, Big Bad in Buffy season 9, and Angel & Faith seems to get their hands full with Whistler and the siblings. No complaints about any of them yet, seems like they could be testing our heroes both mentally, emotionally and physically. I'm happy that Joss is keeping the promise he made in the letter-section of issue 40 of Season 8, and is making this a smaller scale season.