Interesting question.
I guess I would vote for waiting for the man to ask the woman. One practical benefit that was pointed out that I agree with is then you know that he's ready. We all know that marriage is a big commitment for each party and for a man, he has to be ready to take on the responsibility as head of the household for a family. For that reason alone, I can't see asking him b/c how am I going to ask him to take on all that? I say he has to be ready and when he is, I think that most men will ask. Now I also feel like sometimes the women have to let them know that they are not going to be around forever and that the man needs to move it along if marriage is his intention, but I say let the man make that step. It's just the first in many that he must make to lead a family. If I can't count on him to take that initiative and trust that he will, then why would I count on him to take initiative for leading the household on a daily basis. But again, I think there's nothing wrong with a woman bringing up the conversation about what direction they are together and individually headed in.