Becareful about the size of the tires people are recommending. Most of the tires mentioned here are heavy wide tires that don't fit on a modern "road" bike. They work best on cyclocross or touring bikes. I'm not sure about the Trek 2000 but you probably can handle anything larger than 28 without fenders and 23-25 with fenders. In that size the most durable tires are probably Armadillos and Conti Gatorskins are lighter and better rolling but still pretty tough.
Craig