In the beginning of my networking journey, I filed them, alphabetically, in the same box that my business cards came in. I have since outgrown that box and have developed a new system.
1) As I leave an event, or when I get home from the event, I will take a few minutes to write on the back of the card, my impressions of the person that gave it to me. Notes like: introduce this person to John B. Mutual interests (boating, cheesecake, both hate networking, etc.)
2) As soon as possible, but not more than 1 day after, separate the cards with notes from the pack, file them in 'the notebook.'
3) The Notebook: this is an old 3 ring binder from one of my son's school days (trapper keeper). Each Networking group has a separate section in the notebook, there is some paper in there that I use to keep notes about the event, where it was, what kind of event it was, what I thought of the speaker, and any thing else I would like to remind myself of.
4) I recently met someone that makes copies of all the cards he gathers, uploads the information into an 'ACT' style database and includes extensive notes about each person he spoke to. He has 3 office style file drawers filled with binders, containing all the business cards he gathered in the last 30 years. Indexed. With comments.
5) I also recently met someone that uses a photo album as a file system. This works very much like my notebook system.
Whatever your method of filing these important scraps of someone's life, do not simply discard or recycle the business cards you gather. You never know when you will need to contact the person that sells specialized doodads for someone you just met at a networking event that is looking for specialized doodads!