Here are a couple of my favorite, and super-simple, ways to recycle t-shirts that may be a little past their prime. All you need is scissors and an old shirt - an oversized one is great for the headband, and snugger shirts turn into fabulous jersey cowls (or, as I like to call them, "neck tubes").
Sleeve headband: this works best with a larger shirt. I generally cut the whole sleeve off just past the seam and then try it on to see how much more I want to cut off. You may have some curling or stretching as you put it on, but other than that it should retain its shape and edges pretty well, even after being put through the wash.
Cowl: a slimmer fitting old t-shirt is great for this. All you need to do is cut the sleeve and shoulders from a shirt and use the rest to keep your neck cozy and fashionable. (This one's saved me from frustration a few times when I bought salvation army T-shirts that were a great color but too small for me.) If you're feeling super-frisky, you could try cutting down the middle of it, twisting and sewing back together for a Mobius cowl.
Bonus project: t-shirt yarn. Cut any leftover jersey material into strips. Cut a small notch (the smaller the better, as this will stretch slightly) at each end and weave through each other as shown in illustration. Pull the connection tight - the edges of the "yarn" will curl slightly and the connection will become a tight knot. Once you have enough of this stuff, you can use big crochet hooks or knitting needles to turn it into all sorts of great things (bathmats, potholders, welcome mats and more!)