Reduce, reuse, recycle
Once deflated, the flexible plastic packaging can be recycled at local store drop-off locations that accept stretchy plastics (they also accept things like bread, dry cleaning, grocery, and newspaper bags). Many grocery stores provide a bin in front of the store to collect bags and films that are marked with resin identification codes #2 and #4.
Check your local recycling programs for specific regulations: Tossing it all in the curbside bin may seem like the responsible way to get rid of trash, but not every recyclable item can be recycled that way. Aspirational recycling can cause more problems than it seems to solve, and most mixed-use recycling facilities are not equipped to handle flexible materials with the same processes that manage harder goods.
From the drop-off location, BUBBLE WRAP® brand and SEALED AIR® brand packaging is re-pelletized to make a variety of products including trash bags and automotive parts, which can also be recycled. The easiest way, of course, to give these materials new life is to reuse them — in the boxes you send to exchange a gift for the right size or if you happen to ship gifts early in the year.