I mostly hoard greeting cards that I cannot bear to toss into the recycle bin or trash barrel. In order to save space, I usually tear off the front of the card so I can use the artwork again in some other form (ie. gift tags -- see the image below, the stocking tag used to be the front of a greeting card).
However, the one practical use is to recycle the front of the card INTO another greeting card. That is actually very easy to do. All you need is some card stock or blank greeting cards and envelopes. You then just cut the original front to fit on the new blank card. Sometimes I find the written verse in a card to be so very good that I trim off the signature on the card and so I can "borrow" the sentiment and glue it into my "new" card.