Taryn told us about a simple and easy way of cleaning up the monitors of your computers. This also applied to television sets. I've been using something slightly different to clean my monitors. Although it won't clean the grime off screens, it will keep them lint and dust free. The trick involves a lot of air.
If you've ever used paper towels to clean your glasses, you'll know that if you do so repeatedly, you can end up scratching up your lenses. The same thought applies to computer screens and HDTVs. Most laptop manufacturers will give you a microfiber cloth to clean your monitor, but we think that using air will do the same job, if not better since you're not touching the screen.
The trick involves using an air blower, which are used to clean the lenses and mirrors on DSLRs. Any photography store will have a bunch available. The one that I have been using comes from Giottos. Simply use the air blower over the surface of your screen to blow away the lint, hair, and dust.
DSLR air blowers can be used as dusters for sensitive equipment. They work well for screens, televisions, monitors, cameras, lenses, and electronics. If these types of things actually need more of a wipe, then try using the coffee filters or a microfiber cloth.