Gasoline has a certain amount of sediment in it that settles to the bottom of your gas tank. After years of driving around and many fill-ups, there can actually be a fair amount of junk at the bottom of your fuel tank. Your fuel filter will catch a lot of this sediment and keep it out of your car's fuel lines and your engine. However, if you consistently run your car all the way down to empty, you're pulling from the bottom-of-the-barrel and all the extra junk that's accumulated there.
If the sediment gets through the fuel filter (some of it can) it can get into the engine and cause internal damage. It puts debris in areas where it shouldn't be and causes your fuel system and other parts of your engine to work harder. Some people recommend keeping a half-tank of fuel at all times. You may not want to fill-up that often, but make sure that you're not running the gas all the way down to empty. Your engine will thank you for it.