There is not too much wrapping paper out there that is recyclable- so think of some ways that you can re-use it.
Cut out the portions that haven’t been creased- this could be used for smaller gifts, used as a band of color or complimentary design instead of a ribbon, or put into use as a gift tag or card by using a glue stick and a piece of card stock or even a simple index card.
If you have a Serger, think about fabric wrapping and the possible re-use into table runners, placemats, napkins or other holiday decorations. Many fabrics are on sale and if you are looking at wrapping something big- say a baby stroller- that’s a good size that might even yield a tablecloth.
Favorite bows can be saved by using a twist tie and tying them to a hanger for storage. Throw a cleaners’ bag or other plastic bag (preferably clear so you can see what’s inside) and store it some place handy – a closet, from your basement joist or even an attic.
And last but not least- save the good boxes. They can always be wrapped, top and bottom separately, and re-used. You could even make it a holiday tradition, that one gift always has to fit that box- or be an item that is “re-gifted”. Store your cards or holiday decorations in it. Make it fun and interesting.