This one is dear to me since I do this exact thing when I give gifts. I also sew some drawstring gift bags to put my gifts in. Here is a nice tutorial from Zakka Life.
Of course we have all heard of (or used) newspaper, I especially love the funnies for gift wrapping and brown grocery paper bags for gifts (can you say paper or plastic?) but what about using an old map. With the world map changing lately you may have one that is not current anymore.
Here is a recycled paper bow to go with your recycled gift wrap. This is a great use for those old flyers or magazines laying around. Hey you could even use chip bags or sales flyers.
If you are giving a CD or DVD here is a great paper flower case to put it in.
Need a box for your gift, here is a tutorial from instructables on using a cereal box.
To go with all the homemade gift wrap and bows here is a tutorial on gift envelopes which you could make out of what ever you like.
I have found lots of printable gift tags for your gifts:
The point to this challenge is to shop at home and see what you have that you can use, now get to work!