Every year, I take the cards and turn them into gift tags for next year's presents. I can't do it for all the cards: some have writing on the back of the pictures; some are home-made and I can't cut them; some are on too-thick card I can't round the corners of; some are photo cards of people I know; some don't have any images on them I'd want to use as a gift tag; some I want to keep. Most, however, are fair game. The best cards are ones I can make several tags from.
If you recognise your disassembled card among that lot, congratulations, it made the cut. It has been recycled as a gift tag, and next year will be despatched to the paper recycling bin as a used gift tag. Alternatively, I might not use it next year but will keep it and use it at a later year.
One of the side-effects of making cards into tags is that when I wrap the presents up before Christmas, I am reminded of what a previous year's cards looked like. This means that if you send me the same card twice in a row, I notice.
You have been warned.