Try first using ‘toothpaste’.
Squeeze a bit of the toothpaste onto the watch face. Rub it into the scratch with a finger.
Wait a few minutes, then remove the toothpaste with a soft cloth, using gentle, circular polishing motions.
Also, some people blend baking soda with the toothpaste before applying the cream to the watch face. Follow the same general directions, applying the mixture to the crack, then rubbing gently with a soft cloth.
Just remember, deep scratches are not likely to come off with just toothpaste, so you might want to bring out...
The Big Guns
If toothpaste doesn't work or you just prefer to try something stronger, try diamond paste. You'll need to get a small amount of 3-micron paste and also 2.5-micron paste. Apply the 3-micron paste onto the watch face with a cotton swab, then rub with a soft cloth over the face in a circular motion, concentrating on the scratch areas. Wipe this off then repeat with the 2.5-micron paste, rubbing it until the paste is entirely gone.
For crystal watch faces, you may have to try three different grades of diamond paste, 6-, 3- and .25-micron pastes. Start with the 6-micron paste, spread it around the face and use a soft cloth, or use a hand-held Dremel tool with the felt tip. If you use the tool, rotate it in circular motions, never pressing too hard in any one spot. Repeat this with the 3-micron paste, then the .25-micron paste.
If you're not ready to go the DIY route with fixing your watch, you'll also find a variety of products on the market specifically intended to remove scratches from glass and plastic surfaces. These may work well for you if you follow label directions carefully.