Concoct a paste of baking soda and water. You may remember baking soda as that stuff that's been sitting in the back of your fridge for the last five years. Sprinkle a tablespoon of baking soda into a small container and pour in enough warm water to make a thick paste. Scoop up a dollop and place it atop the scratch. Work it in with soft cotton, moving in a circular motion. After a few minutes, rinse the lens with warm water and inspect your work. If the scratches are deep, you will likely have to perform the process a few more times until your scratch says "sayonara."
Take some help from toothpaste. That's right, not only can toothpaste leave you with fresh-smelling breath; it can also remove eyeglass scratches. First, clean with an eyeglass cleanser to get rid of any material on the lens. Next, squirt a glob of the minty stuff on top of the scratch and rub gently into the scratch with a cloth or piece of cotton. Rinse the toothpaste off the lenses after two or three minutes and look to see if the scratch is still around. If so, repeat the process until the scratch is gone. Stubborn scratches can take a few attempts, but it's easier and cheaper than springing for a new pair.
Spray wood cleaner on the scratch. Rub the cleaner into the lens with soft cotton and watch as the scratch takes a hike. Deep scratches may take several attempts until they are completely buffed out. It is not commonly known, but a product that can clean and remove scratches from wood actually has that same effect on lenses.