I have a thing about throwing out paper, especially if it is pretty and in good condition. I save as much of the good pieces as possible, and use them later to re-wrap presents for friends and family.
I even save the paper that flowers are wrapped in, as it makes great wrapping paper.
Another thing that I do is save any box that looks like it can be reused. For example the packets teabags come in make handy little gift boxes, and look great when covered with nice wrapping paper. Another bonus is the little strips of cardboard that frequently separate the teabags. I remove them, cut them into small strips and use them for creating little gift tags often with the addition of images cut off old Xmas cards which I glue on. Then all I have to do is punch a hole and put a bit of ribbon through, or just attach them to the present with sticky tape.
The above photo gives you some idea of what can be done using teabag inserts, cutouts from old Xmas cards, lovely Japanese paper I bought off EBay and silver cardboard (I think it came from a gift box originally. The two plain white inserts are to give you an idea of what they look like originally folded and unfolded. The wrapping paper came from bunches of flowers I received at various times.