I put them into a small shoebox where I keep scraps of paper, envelopes from others, etc and let my toddler draw on them. She always wants to write on something and I don't like giving her an unused sheet of paper to scribble on! Besides I think she likes the variety.
Then I toss 'em! I do keep photo cards though and let my preteen put them into albums. She is very into doing this, organizing photos. I also have a milk crate in my own closet with a couple of memory boxes to keep the odd extra special card or note. I have love notes from my dh, anniversary cards and the like in there, in one memorr box. In the other box I have special things sent to my kids or dh.