It's only a theory, but if your PC is not connected to the mains earth, the chassis (and therefore the motherboard) would be "floating". Essentialy, the metal casing, USB sockets etc of you PC would not be directly connected to earth.
This carries a couple of risks (although slight). If your PC isn't directly earthed, and no peripheral connected to it is earthed, then the whole of your system may be "floating" at a fairly high voltage (100 or more volts). This sounds "deadly", but usually it is not, as the current is not high enough to kill you. What you can experience is a slight "tingle" when touching any metal parts on your system. The possibilty of component damage comes from either plugging in items such as USB memory sticks, or other peripherals. If a peripheal is earthed, you might see a small spark when you plug in the lead. This is because the PC chassis is at around 100volts (not earth) and you are effectively connecting that 100v to earth when you plug in the lead. It may sound dramatic, but it's a very small spark, and is unlikely to do any damage, as hopefully the metal "earths" of the PC and the peripheral make connection before the actual pins in the connector (whatever they may be - USB, DVI etc). However, this is far from ideal, as it is possible that it the the actial pins within the connector that make contact before the earth connection is made. In this case, you are exposing the sensitive input/ouputs of you motherboard to a large potential difference. They are designed to operate a low voltages, not 100 or more volts. I hope that makes some kind of sense.
What is likely to be more of a risk is static electricity. If the PC is not properly earthed, there is more risk that static could cause damage If you are carrying a static charge (see comments/jokes about cats, carpets etc
) amd you plug in something like a USB stick, the PC is more vulnerable to the thousands of volts that suddenly enter the USB port. Some motherboards do have some static protection designed into them, but it can only provide a limited amount of protection.
I may be exaggerating the problem a little, but PCs are generally supoosed to be earthed. Mostly this is for safety, but it is also a reliability issue.
I need to have a lie down now.
