If you're into upcycling or simply can't bear to let your favourite but worn t-shirts go, Relevé Design can tell you how to make t-shirt yarn. Figuring out what to do with the resulting balls of t-shirt yarn may be more of a challenge. I'm less than impressed by the suggested projects at the bottom of Relevé Design's page, and was underwhelmed by what I came up with via Google image searches and on Ravelry. T-shirt yarn is simply too bulky to use in knitwear. People make pom-poms out of them (for what purpose I don't know), weird rope necklaces, lumpy-looking headbands, and kitschy belts.
I think your best bet is to stick with décor items such as baskets, cushions, and rugs. You'll probably be braiding rather than knitting, and you'll need to know how to work with colour and have a good eye for design in order to get attractive results, because you're going to be working with small amounts of each colour. The classic braided rug seems to be the most generally successful t-shirt yarn project. The beautiful rug above was made by Meg McElwee of Sew Liberated. I bet it feels awesomely soft and cushiony to walk on.
If you've made a successful t-shirt yarn project, feel free to link to it in the comments!