If you would overexpose your
image, your histogram would look like this: too many highlights, no darker
tones, and you can guess that you have lost information: light tones have
become lighter than the camera can handle and have been stored as completely
white. You should re-shoot with a smaller aperture or a shorter shutter time.
On the other hand, this is how
under-exposure looks like: no highlights, the histogram is shifted to the
left, and lots of information from the image will be missing because the chip
in the camera didn't catch light. Re-shoot with a larger aperture or a longer
shutter time.
There's a technical argument around histograms that basically says that there is more information in the higher tones of the image in a digital camera - so, if possible, you should "expose to the right", meaning that your histogram should be shifted a bit to the right, but not too much. Of course, the histogram shown on your camera is an average of all colors - it might be that even though the average color histogram looks fine, a single color (red, green or blue) histogram would show over- or underexposure. Therefore, "expose to the right", but realize that over-exposure of individual colors is possible - better be safe than sorry so take an extra shot that is 2/3rd or a full stop less exposed, so that when you get home and evaluate the individual color channel histograms, you have something to fall-back to when your optimal exposure turns out to be overexposed for a single color after all. Lots of digital cameras have auto-exposure bracketing, and I use it a lot (bracketing 2/3rd of a stop to both sides).
When shooting in auto mode, try overexposing 1/3 stop to shift your histogram just that little safe bit to the right. Of course, experimentation is key - the great thing about digital is that experimentation is all for free!
Sometimes there's more in the image than your camera can capture - a digital camera will capture around 5 stops of dynamic range, and if the dynamic range of your subject is larger than that, you will have to make a choice to let the highlights or the dark tones fall off. The Canon G5 has a built-in Neutral Density filter that will compress contrast, so that is another option (external, 'classical' ND filters, of course, will work just as fine on digital cameras).
Keeping in mind that a histogram on your camera usually represents 5 stops worth of dynamic range helps you calculating the correct exposure when correcting a histogram: for example, the underexposed histogram above shows that more than a fifth of the highlights aren't used, therefore increasing the exposure by a full stop will move the histogram 20% to the right, where it still 'fits'. More than that (1 1/3rd stop) and you risk overexposure, less than that and you're not exposing "to the right" enough.