My usual recommendation is to start with water (preferably distilled... I generally just use tap) and a soft lint-free cloth.
If you have something stubborn, try increasing concentrations of isopropyl ("rubbing") alcohol mixed with water. Available at any drugstore; just make sure you get stuff that doesn't have anything else mixed with it. If you can only find ~70% concentrations, ask at the pharmacy; in some places they can't put 90+% out on the shelves. This is useful if there is actually something on the screen that you're trying to get off (other than just dust).
If alcohol isn't cutting it, the next thing I would try is an ammonia solution (ie, Windex), or some kind of commercial LCD/electronics screen cleaner (some are isopropyl and/or ammonia, but there are others).
The risk of using anything much harsher than water is that you can potentially damage anti-glare coatings on the screen. The user manual for your LCD usually tells you what they recommend using.
Do not use acetone (nail polish remover) on LCD screens; the screen fronts are generally plastic, and will be discolored and/or weakened/dissolved by acetone. It's good for use on circuit boards, and can be used on CRTs made of glass, but don't use it on LCD/plasma screens, or most projection sets.