Reuse: Shipping services like Mailboxes, Etc. will often accept peanut donations, as will many stores and businesses that do a lot of shipping. If nothing else, list them on the Freecycle Network, since someone in your area is bound to be moving or shipping something.
Or reuse them yourself. Store packing peanuts in an old pair of pantyhose to keep them from over taking your house until you're ready to ship them off to someone else. Cut a hole in the toe -- if there's not already one there -- and tie it off with a twisty-seal for easy peanut dispensing.
Recycle: More and more recycling programs are accepting packing peanuts, but make sure you put them in a bag or box so that they don't escape and invade the neighborhood.
Refuse: If you detest packing peanuts as much as I do, ask mail-order companies if they use them before you agree to place an order, and encourage them to use the new biodegradable variety.
Sometimes companies, particularly smaller outfits, will agree to ship your order with shredded newspaper or some other more eco-friendly substitute instead.
Make ice last longer: Put packing peanuts in a sealable plastic bag and place on top of the ice in your ice chest. The ice will last longer and everything will stay colder.
Potted plant drainage: Substituting packing peanuts (the non-biodegradable variety) for gravel in the base of potted plants not only provides good drainage, but it makes the containers much lighter and easier to move.
Stuff a costume: Whether it's Santa's belly at Christmastime, a goblin for the front yard for Halloween, or a scarecrow for the summer garden, think packing peanuts whenever you need some lightweight costume stuffing.
Floating key chain: Thread a few packing peanuts on your key chain if you're going boating or to the beach. They'll keep your keys from sinking to the bottom of the deep blue sea.
Perfect pet pillows: Use packing peanuts to stuff a pillow for your pooch or a cushion for your kitty.
Deck the halls: String up multicolored packing peanuts instead of old-fashioned popcorn and cranberries for some festive yuletide decorations. Nothing says "Happy Holidays" like repurposing would-be throwaways.
Home Insulation? No, but maybe an entire home: Unlike foam insulating materials used in home construction, packing peanuts have not been treated to make them flame retardant, so they shouldn't be used as insulation.