I chucked most of them when I took down the decorations. I have 5 or 6 in the end table drawer that the kids like to get out and play with. They're all from friends or family (with kids or dogs, lol now that I think about it)
I put them up with the Christmas decorations. I save them all each year and put the on a binder ring. Each year has its own ring. I put them out each year with the decor. It's fun to see the changes to families over the years.
I hate throwing away the pictures, so I put them in a binder. That's a new thing I just started. I add any photo cards we receive - birth announcements, birthday invites, etc. My plan is to keep adding chronologically. Some day my grandchildren will find it and think I was insane.
Christmas cards get hung up for the season and thrown away when the tree comes down. I keep one of ours to save but I don't save others.
This exactly with holiday cards, since we get so many. With photo birthday invites though, I give them to DS to keep in a little drawer in his playroom. Its always kids he is close to, so he enjoys pulling them out and looking at his friends.