Twilight, of course, is the Forbidden Fruit, as all of you have said.
I know the cover had nothing to do with the series, New Moon, to me, means this:
Throughout Twilight, characters mentioned that Bella smelled "floral" in some way. Therefore, the flower on the front of New Moon would be Bella herself. And the flower seems to be splattered with blood, so to me that could represent her falling apart with the loss of her lover. (What do you guys think? Does that sound plausible?)
Eclipse's cover showed Bella's difficult choice between Edward and Jacob--her life was going in many different directions.
Breaking Dawn--Well, at first, it seemed, since it showed the queen on a chess board, that it would represent some very strategical decisions. Like the queen (Bella again, of course) was cornered (checkmate), and a wrong move could cost her and the ones she loves their lives. I don't know. That's what ran through my mind.
"It makes me... anxious... to be away from you."
-Edward, Twilight, p. 188