It can really be a pain when you are chopping up a strong onion, making your eyes water and burn.  This is due to a gas coming from the broken cells in the onion caused by cutting them.  But, knowning this also gives us the answer to stop it.

The gas which is generated by cutting usually goes up into your face.  If the onion is higher than your eyes, it does not reach them.  Of course, you cannot easily cut an onion that is above your head ;)

The answer is to move the gas way from your eyes.  Some will cut onions under water to help reduce the effect.  Others have said they use a candle near by the cutting and it sucks the gas and burns it up, but that would be a bit of hassle every time you wanted to cut up an onion.  A few people mentioned running water nearby where you are cutting which can help draw the gas way, but at the cost of a lot of wasted water.

A simple method is to keep a small battery opperated fan on your counter top out of the way and when you want to cut an onion, turn it on and have it blow "away" from the onion you are cutting.  This will pull the gas away from you so that it does not rise to your eyes.