No! You can send them to St. Jude's Ranch for Children, and let the kids there make them into new Christmas cards! I just sent them a big batch of cards today (or I would have, if the post office had been open), representing several years of Christmas (and other) cards... I also bought a pack of 10 birthday cards, which I took to work for those surprise office birthdays...
if you want to recycle your cards, you can get the how-to info by following the links above, or here's the address right here! They only want the fronts of the cards, so feel free to cut the cards in half and only send the fronts to save on postage:
Recycled Card Program
100 St. Jude's Street
Boulder City, NV 89005
Recent cover scan I added to GCD:
Tank Girl: Visions of Booga #3