If you have a
flat panel monitor, you should be extremely
careful when cleaning it.
Normal CRT-based monitors have a piece of glass anywhere from half an inch to a full inch thick on the front. This makes them rather strong and nearly impervious to damage. Flat panels, however, generally have a thin plastic anti-glare coating over the actual glass LCD panel. The glass that makes up the front surface of an LCD panel is very thin, so it bends easily under pressure.
If you apply too much pressure to a flat panel, you can damage it severely. Therefore, flat panels should be cleaned very softly, and since the front surface is plastic, with a soft cloth as it will scratch much more readily than a glass CRT screen. You should also avoid using solvents to clean flat panels; they can damage the plastic anti-glare sheet.
Cleaning the flat panel while it is on and displaying an image helps; you should avoid pressing hard enough to discolour the image.