GreenWeaver-I like the idea of a memory box, but you can also make a Christmas card collage and take a picture of it.
This is something that your children can help you with and is a lot of fun. You simply get a poster board and cover the entire board with the front cover of the Christmas cards.
You can keep the collage or simply take a picture of it and either make an ornament out of the photograph to commemorate that year or keep it in an album.
You can then throw away the collage or keep it and put in your garage. This way every Christmas you can bring out the collage and use it as another Christmas decoration.
You can even start a tradition and do this every year. I know that there is some beautiful charity Christmas cards that I would feel guilty throwing away.