OK, the method above can deal with those occasions where an unfortunate spillage is obscuring your view. But what about the caked-on layer of grime that has built up on your monitor, if it's over a few months old. If you smoke, or live or work in a large city, you'll get plenty of this tar and diesel gunk yellowing up your screen (didn't you know that the Jukka Dim Theme was supposed to be pure white?!) Here is a labour-intensive yet safe and effective method :

You will need one large, expendable and fairly coarse cotton rag (I recommend a handkerchief), and one standard black computer power cable - of the sort with a wall plug at one end and a female three-pronged plug at the other. Take the end that you stick in your PC and wrap the rag tightly around it. You want to have one layer of cotton stretched over the hard edge of the plug.

Holding this with your index finger outstretched gives you a powerful scraping tool. Put a pure white background image on your screen (preferably this should be the only thing on screen). Now start rubbing, until you have no bits of dirt left. Pay particular attention to the corners and edges. You will intermittently have to reposition the rag on the socket as it will have picked up a nice sliver of pure evil. This method also works on the flat areas of the monitor housing, although a damp cloth would be easier for that.