One of the questions I get asked most often relates to scratches on watch crystals. If the crystal in question is 'sapphire' ( aka. aluminum oxide or corundum ), the only thing that will scratch it is a diamond and there's no reasonable way to remove even the most subtle of scratches from it.
A few years ago someone came up with a crystal scratch removal kit that had a diamond-based compound as a part of it, the idea being that you could 'cut' the scratched crystal with the diamond compound to remove scratches. The results, unfortunately, were somewhere between bad and atrocious - the problem being the distortion causing waves in the crystal created as the scratch removal process was underway.
My advice is that if you've got a watch with a scratched sapphire crystal, you do some experimenting to figure out what's scratching it with the old scratched crystal still in place (hint: if you sleep with someone who wears a diamond - don't wear your watch to bed!). After solving the mystery, head to a reputable watchmaker (or, if you have the tools and inclination - roll up your sleeves) - buck up $150 or so - and have the crystal replaced.
If the crystal is mineral glass, the cost of replacement will be much more nominal but it will be much easier to scratch since mineral glass is much 'softer' than sapphire crystal. Again though, there's no good way to remove a scratch from a mineral glass crystal - when it gets annoying - replace it!
Lastly, if the crystal is acrylic (plastic), you can remove almost any scratch easily with some Polywatch and a soft microfiber polishing cloth. Acrylic scratches easily and can be restored just as easily.