Bella: ISFJ - One of her major character traits is how much she likes constancy (dom Si). She spends the whole first book longing to go back to Phoenix (to return to what she's used to) and other characters comment on how much she likes stability, how much she hangs on to things, how much she's like Charlie (an ISTJ). She also takes care of both her parents, which seems much more like an IFJ than an IFP. True, she's angsty and romantic and feels like she doesn't fit in, but I've known ISFJs like that, and I also think it's more related to her being a teenager than her type.
Edward: IxTJ - His traditional streak seems SJ, but the way he tries to control Bella (like by taking the engine out of her car) seems like an unhealthy INTJ.
Alice: ESFP - I agree with Little Linguist that she's an S. All of her interests are concrete (fashion, planning parties, fast cars). Which isn't to say an N can't like those things, but I'd also expect to see her show some evidence of abstraction if she were an ENFP, and she doesn't (aside from her power, which doesn't count since, as LL said, she uses it the way a normal person would use their eyes or ears).
Jasper: INTJ (maybe a calculating INFJ?) - Even though he can control people's emotions, he seems driven by logic. He uses fear to control the lawyer in the last book (versus Bella, who as an F approaches the lawyer with kindness). When Bella gets turned into a vampire, he's also the only one who is suspicious of her ability to control herself and isn't concerned with the fact that this hurts her feelings. Maybe I could see ENTP, but he seems like too much of a subdued loner to be one.
Carlisle: ENFJ
Esme: ISFJ
Emmett: ESTP
Rosalie: ESTJ
Renee: ENFP
Charlie: ISTJ
Jacob: ESfP
Sam: ISTJ
Leah: ESTP
Aro (head of the Volturi): ENtP?
Wow, that was a lot of analysis for some very bad books, lol.