If the plastic bit at the end falls off, just cut off the frayed part and dip the end into molten wax from a candle. I can't say I've tried it yet though, even that's so much trouble that I just live with the frayed end.
Heat-shrink tubing is perfect for replacing shoelace ends, if you happen to have some lying around (or have a friend who tinkers with electronics you can blag a bit off).