Lately, I've noticed lots of articles in magazines and on the Internet about reverse applique. It's a great technique to use on t-shirts, especially if you have a favorite that has a small hole or stain that you want to cover. Basically, you sew a fabric patch on the back (wrong side) of the shirt, then trim out the front of the shirt, revealing the patch underneath. T-shirts don't really fray, so you can leave raw edges and not worry about it.
Yesterday, I worked on a sample for my (new) adult sewing class. The t-shirt was a men's XL for $3 at the thrift store, and I patched it with a couple old t-shirts and some yardage I bought recently. Of course I couldn't resist spicing things up a little: I used a gel pen to doodle on the light pink fabric before I sewed it.
The latest issue of Sew Simple (volume 12) has a nice article about reverse applique. I also found a great, straightforward tutorial here at the blog "that *darn* kat." The only tip that I would add is that if you haven't sewn knits before, this is a good way to start. Use a short stitch length, go slow to get around the curves, and enjoy the results!