Even though I believe that one good conversation beats 100 business cards, collecting cards still has its place.
First, while people won't necessarily remember you after a single encounter, my philosophy is that you need three casual encounters to build familiarity. Even if a person doesn't remember you after an initial meeting, it still counts towards that three meeting threshold.
Second, collecting business cards lets you pick which folks to follow up with. Simply sending an email or even a LinkedIn request doesn't build a relationship. Rather, you need to schedule a call or in-person meeting (assuming mutual interest, of course; if someone dodges your request, accept it for the rejection it represents, rather than going stalker on the poor sod). Surprisingly few people follow up! When you do send your request, offer some specific times so that you don't force and endless and annoying back-and-forth for scheduling.
Remember, collecting cards is just this first step; the real work is in building relationships.