According to Bruce G. Marcot, Ph.D. Research Ecologist who attempted to answer this exact question, if a family received 365 newspapers per year and recycled them, they would save approximately one half of a tree.
This is a quote from Bruce G. Marcot, Ph.D's research at the USDA Forest Service, PNW Research Station in Portland Oregon:
"For example, let's say that an average newspaper weighs 2.2 pounds (my complete guess!) or 35.2 ounces, then N = 26,553.6 / 35.2 = 754.4 newspapers per tree. Then, over a year's time, if one family recycles 365 newspapers, they save 365 / 754.4 = 0.48 trees, or about half a tree. If the families of all 30 students recycle, then you're saving about 15 trees per year, which is enough habitat for two colonies of Acorn Woodpeckers, or half a dozen nests of Brown Creepers, or lots of other things!"