I work a lot with home theater gear (LCD, Plasma televisions) and screen cleaning often comes up.
The guys at HDNation have a show about screen cleaning where they talk about 'polishing' a spot on a screen, using cleaners that melt plastic, penetrate glass (ammonia) and dissolve anti-glare coating. The thing that seems to work consistently is a 50:50 water and alcohol solution (using Deionized/purified water) and the micro-fiber cloth. (See link below).
Monster sells a "Screen Cleaning Kit" for about $15 with a spray bottle of 50:50 water and alcohol and a micro-fiber cloth. This is probably best for most people.
http://revision3.com/hdnation/screenclean