I try as often as possible to use cloth dishtowels instead of paper towels. But while dishtowels are great for drying my hands, they often get too damp to dry my dishes sufficiently. That's why I can't wait to try the Twist Euro Cloth #20, which is described as a cross between a super-absorbent sponge and a lightweight paper towel. (Thanks to Apartment Therapy Chicago for the tip.)
Obviously, these have the benefit of being reusable, but they're also biodegradable once you finally have to toss them in the trash. It's also antibacterial, and you can freshen it up by washing it in the dishwasher. You can buy the Euro Cloth in a number of grocery stores, including Wild Oats and Whole Foods, and you can also get a pack online for $6.