I hate throwing out my children's birthday cards. I won't do this for every year of their lives, just the milestone years. For my son's first birthday, I make some zigzag pockets using some left over stickers, small photos that i haven't used and also his invitation to his party. I also used some left over border edges in primary colors and paper that I had not used up. This held ALL of his birthday cards for his first year and when he is older, he can go back and see who came and read all the beautiful messages left in these cards for him. I also document on the back of each card what he received as gifts.
Note: depending on how many cards, you will need to use sturdy cardstock such as Coordinations or Bazzil, otherwise it will rip with the weight. It also does make a bulky page.