A while ago I attended a networking event, and I was struck when the attendees I met asked for my business card. I was not concerned that they asked for it, but rather when they asked. My card was often requested as we were initially shaking hands, and another time I was even interrupted while attempting to introduce myself!
This may sound like a trivial gripe from an anal-retentive guy, but it left a non-trivial impression. I had the feeling that these people were card collecting, and not necessarily interested in learning anything about me. My impression was reinforced after I obliged with my card: the person's eyes wandered about, looking for his/her next networking victim. Clearly it was a numbers game for some of these attendees.
My advice is always to get to know the person first, and ask for a business card when the conversation winds down...if it makes sense to do so. Networking is about building relationships, not about collecting contacts. Make the right first impression by first impressing them with your genuine interest in him/her as a person.