LCD and plasma screens — the ones on laptops, newer desktop computers and televisions — are not as tough as glass CRT screens. They can be scratched fairly easily, so it is very important to use a soft cotton or microfiber cloth that is completely free of dirt. These types of screens are often plastic, or have an anti-glare coating that may react badly to household cleaners such as Windex. In particular, avoid any cleaning liquid that contains acetone; ethyl alcohol; methyl chloride; ethyl acid; or ammonia. If plain water won’t do the trick, mix water with white vinegar in equal parts.

TIP: If you have a house cleaner at home, or a cleaning staff at work, make sure they know that they should never use Windex or similar glass cleaners on your LCD screens. That includes laptops, desktop monitors, and TV screens as well.

Do not scrub or press hard on a LCD or plasma screen. It may bend, stressing the tiny wires embedded in the plastic screen and possibly breaking some of them. Then you will have permanent damage, like a dead pixel that remains dark all the time or a “hot” pixel that stays lit when it should shut off.

A lot of different screen-cleaning solutions are on the market. They’re all pretty expensive and don’t do the job any better than vinegar and water. Likewise with “specially treated” cleaning cloths. Cotton underwear or handkerchiefs are just fine. Many hardware stores sell inexpensive bags full of lint-free white cotton cloth scraps used to apply finishes to furniture; those work well for screens too.

Cleaning the case of a monitor requires a bit less gentleness but just as much attention to drips. Do not let cleaning solution drip down into the circuitry! A desktop monitor collects the most dust on its top, so pay attention to that area. It’s generally unnecessary and ineffective to try and blow or vacuum dust out of the inside of a monitor. – Internet Tourbus