This is a topic I've always got a bit 'uhh, I dunno' about.
In a perfect world, this wouldn't be so much of an issue. But roles are mixed up now, whether we like to admit it or not. Men don't want to come across as 'neanderthalic' and 'I want you, you come' etc, yet at the same time, with all the flirting us girls do, they never seem to be able to work out how serious we are about them.
Same with women. They are just as bad at reading men sometimes (or maybe it's just we don't trust our intuition as well as we should, and think 'oh he's just being friendly), and don't want to come across as 'persuant' cos that seems to strip away 'femininity' in some peoples minds.
I think there are different times where it IS appropriate for a woman to make a move. Sometimes it's as simple as a small conversation about being open on your feelings for one another, sometimes it's a little more 'overt', such as asking the guy to a dinner, a group event, etc. I think Ruth gave a great example of woman taking the initiative, and still did not give off an 'unfeminine' air. Remember - guys aren't good at starting conversations about deep issues (generally), so sometimes, it's good for a girl to get the ball rolling with these kinda issues, and then leave it in the guys hands.
I think the best time this whole pursuing thing worked for me, was this relationship I've got now (that's serious, and will almost definitely end in marriage). It took me standing up and saying, listen there seems to be a miscommunication here about what our relationship is, let's take this time apart to work out what we want, and what is Godly, and on (insert date here) let's go out and resolve this once and for all. It was me who put the words 'out there', but it was him who eventually had to pursue me, and kinda 'prove' that he was the right guy for me, and that the changes that would have needed to be made for a successful relationship to happen, had happened. These changes happened slowly, and not completely 'overtly', but I could see them, and in that way with address behavioural and communication issues, he pursued me, and ultimately began a loving committed relationship with me. So, in regards to this topic, I guess we both pursued each other - I got the ball rolling from my end, and he continued it, to such a point where a Godly, loving relationship was seen as beneficial for us, and began.
I for one can certainly vouch for this type of pursuing!
Sasch