If you do any business in Asia at all, especially in Japan, it will be extraordinarily awkward for you if you get rid of your business cards. You will come across as someone who doesn't know their business culture, or--depending on how well known your company is there, and how often you work in Japan--as someone who just doens't care that you're being rude.
The exchange of business cards is a ritual, in which you carefully present your business card to your new colleague, and an exchange takes place. This is a key part of introducing yourself. The first time I went to Japan, I didn't bring enough. It was absolutely mortifying to run out halfway through the trip, because you exchange business cards with absolutely everyone you meet. I went as my organization's representative, as we were participating in an international exhibition. I had to exchange cards with my translator, my escort, the representative from the newspaper sponsor, the multiple representatives from the airline our cargo was transported on, the customs brokers we worked with--and that's before I even met the people who work in my field! I went through 40 business cards in two days. When I got back, I mailed cards to those people who hadn't gotten one. I've found that this level of exchange also holds true when working with China, Cambodia, and Thailand.
As for the idea that they're useless--I disagree. When I get back from one of these trips, I take a photo of the business card and upload it to Evernote, along with a note of on which trip and project that person was part of. Eventually Evernote gets around to OCR'ing the text in the card. I now have a record of everyone I've met through work which is mine. Not my employer's, mine, that I can take with me if I leave to go somewhere else.