Electrostatic Discharge Protection is a good thing. Depending on the environment, you can generate a substantial charge. By the time you see or feel a spark, you're already at tens-of-thousands of volts.
As often as not, you don't outright kill a/the chip; you destroy some of the internal paths, or erode them (make 'em thinner). The effect is glitchy random failures.
It's not so much that you have to be grounded, you and the components you are working on should all be at the same potential ... "ground" being the easiest to accomplish.
The other thing to remember is that if the power cord is plugged in, and the power switch on the PS is not in the "OFF" position, there's power being fed to the motherboard (the PCI bus, The AGP slot, the RAM, the processor, etc). If you plug something in with power applied, even standby power, it can also damage the component or motherboard. If your power supply does not have a power switch on it, then you should unplug the power cord before adding or removing components.
With the power cord removed, you still need to equalize the charges between yourself, the component, and the place you're plugging the new part. A wrist strap tied to the chassis is the easiest way to make sure you don't zap something. If you don't have a strap, then make sure you touch the chassis periodically. Don't remove the component from the anti-static wrapper/container until you do.
ESD protection is a small, easy thing to do and might save you many headaches later on. Systems these days are more tolerant, but why take the chance?
FWIW
Scott