Going to take a few stabs:
Buffy: XSFP. There is really no need to even to pinpoint Buffy's IvsE anyway, because her energy clearly comes from somewhere else entirely, and she can muster it in full force with the use of her will+something sacred to the Slayer.
Willow: INFJ. not sure how people can say she's a P. she's always so on the ball with her various duties and hobbies. We also know she's an incredibly rare type, as those mysterious tester dudes usurped her and OZ, seemingly to recruit them, in one of the episodes. I'm guessing that because of her intelligence, she tests like a T would. She has many Mastermind qualities, but throughout the season, she proves time and time again she is ruled by her emotions.
Xander: ESFP. It makes sense to me that he is so similar to Buffy. Throughout the series, he works as her foil, in many cases, calling her out at the drop of a hat. At the end of season 4, he takes the place in the magic circle as Buffy's "Heart" and she echoes this sentiment again in season 7. Buffy trusts him more than anyone else to take care of Dawn, which means a lot. I'm not there yet in my re-watching, so I can't cite the episode yet.
Giles: INTJ. What else could he possibly be? Process of elimination works better than any other method with him.
Cordelia: ESTJ. Cordelia continually acts as the voice of reason in the beginning of the show, despite her ditzy packaging. She tends to say what the average American is thinking, in this way she embodies the traits traditionally valued in our country.
Angel: ISFJ with a soul, and ESTP as Angelus. He seems to change coretypes depending on whether or not he has a soul. When he is Angelus, he is very much a typical evil Artisan. When he has his soul, all he cares about protecting everyone, especially Buffy. Don't forget about the the "needing to be needed" and the classical moodiness and sulking associated with ISFJ's.
Spike: INFP as a human for sure. As a vamp, I'd say ENFP. Not much change. He takes awhile to really come into his personality, but I think his situation is best described as coming full circle. By the end of the series, he truly is a Champion. He also closely resembles his human personality, and I don't think he needed his soul for this to eventually happen. Even in the flashback episodes showing him as a newborn vampire, he was clearly different than Angel. Strangely he still had his emotions, his ability to love, and fear. Basically, he still had human in him, and therefore his human personality.
Faith: ISTP. In one episode in Season three, Angel remarks "you and me Faith, we are alot alike." What he meant was, you act like I do when I'm evil. There is a silly OkCupid test that uses the Myers-Briggs, but renames the types with "bad" names. ISTP's are called "the Criminal" on that test. Fitting. I think Xena is also an ISTP, and these two act the same when they are being naughty.