There are many different options for frugal gift wrap, and readers at this site probably know most of them- recycled newspaper or comic strips, old maps, cloth bags that can be re-used season after season, butcher paper that the kids decorate, or skipping the wrapping paper completely and going for a sort of scavenger hunt, with clues leading up to the final hiding place where the present is, or using part of the gift for the wrapping, such as a receiving blanket to wrap a baby gift.
Sometime last year I was at a thrift shop and bought a roll of old wall paper for .50. It was a huge roll, and it was old enough that it was the kind that you had to apply the paste separately. My intention was to use it for shelf paper, but my husband found it first and has been using it for gift wrap. It's his new favorite. The paper is flexible enough to fold and wrap around corners with ease, but it's thick enough that it doesn't tear easily, and it's not see-through. The vintage pattern (a sort of red on yellow toule print) is striking, and it looked great under our tree, but looks equally pretty for the spring birthdays our large family has coming up (we have so many that I once joked to a single male friend that I calved in the spring, and he pointed out that if he said that, or if he laughed too hard, he'd get hit).