Also, lets not forget, that using flash "off camera" on a stand, or with a bracket is another way to help avoid red eye. If you're using the "in camera" flash, of course, the only options are in post processing.
As touched upon, the reason for red eye is the flash illuminating the shiny retina of the eye. When the flash is placed close to the lens, the light reflects directly back causing the red eye effect. Once the angle is changed, the reflection is directed away from the lens thus removing the problem all together, and the reason Dougs suggestion is helpful about having people look away from the camera. The reason preflash, or adding brighter lights helps is because it causes the pupil to close more, reducing the chance for reflection, but still isn't always 100% effective. And bouncing has other advantages as mentioned by alexphotos. A good flash with accessories is a great investment, which can pay off with better photos for years. Try purchasing one that you'll be able to use with the complete system of cameras if you intend to upgrade in the future. Like lenses, try getting the best possible one you can afford from the start, and you won't be needing to upgrade it later on too. Just one more reason to stay with better name manufactures who have produced "pro" market equipment for years.
Enjoyable, and informative thread everyone, thanks!