There is a site called Printsew.com that lets you do just that...print out patterns. It saves you shipping charges, as well as the cost of driving to the store for a pattern. But it does mean printing out pages and pages...and pages. Since the patterns are given on 8.5 x 11 sheets, even a simple pattern can easily run over 50 pages.
I've been sorting out and throwing away old papers. I was just about to toss about 100 sheets of a printout from our insurance company...until I had an 'ah-ha!' moment. Why not use the papers for my patterns? Yes, they are printed on both sides. But there isn't a lot of writing on pattern pieces (and I never read that writing, anyway), and anyway, it's free.
So I would suggest looking over any 'old' papers you don't want, ones that are in good condition (in other words, they won't jam up your computer.) Use these for printing out simple things such as patterns for appliques, and save the blank paper for 'good' use.