Newspaper – Don't laugh! My cousins and I did this when we were in college and we barely had enough money to buy gifts. Use the Sunday comics section and your package will be covered in lots of colors. You can always add a ribbon or bow; both of those items can often be reused.
Reused gift bags or paper – If you receive a present in a gift bag, save the bag and use it for a gift that you're giving. And, if you open a present carefully, you might be able to reuse some larger sheets of wrapping paper.
Cloth – If someone in your family sews, you might be able to use some larger pieces of scrap material to wrap a gift. An alternative that costs a little bit of money is to purchase some remnants of material at a local fabric or craft store.
Festive towels – This choice costs a little bit of money, but it gives a the recipient an extra gift—and the "wrapping" won't be tossed in the trash. You can often find festive holiday hand towels at discount stores. Or you can wait for the post-holiday sale and buy some to use next year.