Now this is one I continue to get different opinions on, from men and women. Many guys I've spoken to still prefer to ask women out; it feeds the idea of a chase.
Other guys? Well, they seem to like to not do the heavy lifting (a little lazy, in my opinion).
Meanwhile, women also land on both sides of the coin. Some still like to be asked out (admittedly, I'm of this school of thought) while other take the bull by the horns and decide to ask a guy out.
Truth is, whatever your preference, it's the idea of a chase that makes dating fun.
I've asked a few guys out in my day. Although in hindsight, those situations haven't fared well for me. Not to say they don't work.
Personally, these days, I play the game by dropping hints. And if it's right, then he'll ask me out. If not, then there's no way it would have worked.
Besides -- Not such a fan of lazy guys. :-)