Scratches on furniture can often be camouflaged by any of a number of simple techniques, especially if the scratch follows somewhat the grain of the wood.
When there is no stain on the wood, so the finish is actually the natural colour of the wood, simply putting a bit more finish over the scratch can blend it in. Minwax's Wipe-On Polyurethane is an excellent product for touching up such finishes, or even for putting a light protective coating over the products listed below. The advantage of a wipe-on finish is that you can put it on thin enough that it blends easily into the rest of the surface, where-as a brush stroke of a thicker material would show. The disadvantage is that this is not considered a finish for heavy foot traffic, so you may have to wipe on many coats for floors, but if it is just a scratch wide, that is not really a problem. Use this same technique for a scratch in a finish that does not penetrate the stain.
The traditional method of matching colours for scratches that have gone through stain and exposed un-stained wood below is to use coloured wax crayons. Although kids colour crayons can be used, wax crayons specifically sold in paint stores have much closer and more consistent colours. Note that you can kneed together several colours to get a closer match. The problem with this technique is that it sits on the top and cannot be covered with a clear finish because it is wax, so this only really works for things like chair or table legs or skirts. It is however waterproof and you can damp wipe the surface without getting water into the wood under the finish.
BLEEDING THE ORIGINAL STAIN INTO THE SCRATCH
A bit of a revolution in hiding scratches was a product called Scratch Match, which has unfortunately dissapeared, but I will leave the description here in case some brilliant person wants to bring it back to life. One clear tube to match all colours! So how does it do it? If you have scratched through the stain it means that you have definitely scratched through the protective finish. When you apply Scratch Match, it actually flows under the finish and causes the original stain on both sides to bleed out into the scratch, essentially re-staining the wood with its original stain. It won't bleed far, so this is only good for narrow scratches, not large spots. The Scratch Match evaporates off and you can apply a protective finish, like Wipe-On Poly and the end result is as good as fixing a scratch that was only in the finish. But as I said, this miricle colour matcher is no longer available.
STAINING JUST THE SCRATCH
The next best thing to the old Scratch Match is new covering product made in Canada from the company Trade Secret: Scratch Remover. This comes in two colours, one for dark wood and one for light wood. Just wipe in on and minor scratches dissapear -- working better in scratches that flow with the grain and design of the wood than across the grain. They also sell liquid touch-up markers (like a stain in a felt pen) that you can layer on to blend colours or darkness. These can be finished over. And they have quality wax colour sticks for deep scratches, but these are wax and cannot be covered over with a protective coating.
One radio listener recently asked about removing cigarate burns from a floor. Here the heat has definately damaged the finish, maybe even burned the wood. I always start with a sharp scraper, something like a pocket knife. Very gently I scrape away the problem area. By being careful I may discover that it did not touch the wood, maybe didn't even bother the stain on the wood. If that is the case, simply put a bit of finish, or many coats of Wipe-on-Poly over the work area. If it does touch the stain and the wood, scrape until the burn is gone and feather out the hole so there are no steep edges. Then use the Trade Secret touch up pens to gradually get as close as possible to the surrounding colour. The wet colour will be closer to the colour under a protective finish than the dry colour. Play with scrap wood, or inside a closet to see just what combination of liquid applications works best -- always working from lighter up to the dark colour. Put a protective finish on your test patch to see the final colour before starting on the open floor area.
AVOIDING STRIPPING AND SANDING
Of course none of these techniques actually remove the scratch and under certain lighting, it will still show. They are always more successful when the valley of the scratch itself goes with the grain rather than against it. But they are always worth a try, because the next alternative is to sand or strip it all down and re-finish the whole piece of furniture or the entire floor. However, filling the scratch with a finish topcoat can actually level it out. You may have to use a very fine sandpaper to flatten the final coat, but then pass over the whole thing to put the shine back with Wipe-On Poly.