As I always have to say on threads on this subject, the Germans don't "do" cards. So between us we might get two or three per year. We have a frame around the mirror in the hall where we pin photos of events during the year, theatre tickets, birthday cards and the like. These go in an album at the end of the year and then we start again. I wish I'd thought of doing this earlier. I only started doing it about 5 years ago.
However, if you do have birthday cards to spare you could use them as bookmarks, or have the nicer ones framed. It is usually form the dedication inside that you would like to keep them, though. I think, in theory I would like to be organised and keep them in a scrap book, but in practice, I will keep them in a pile somewhere or in a drawer, and throw them away at a later date.
My mother had kept all the postcards she received from my eldest son on his travels. I recently showed them to him and he had a lovely time re-reading them - he said it was like a time machine! There were the cards that I had sent,too the pile was over 3" high!