LCDs are a "sample and hold" technology, basically meaning the TV will create an image and hold it for 1/60 of a second or 1/120 of a second depending on the model. LCDs will hold the pixel value constant for the entire 60Hz or 120Hz refresh. This is the reason why LCDs don't flicker but at the same time why they blur.
Plasmas on the other hand don't sample and hold but use "pulse width modulation", this is one of the reasons why plasmas have less blur but have some flicker but most people don't notice it (but you obviously have).
You will notice in the future that LCD manufacturers will have to introduce some form of "flicker" in order to control motion blur, you can already see this in the Samsung 81 series, LED backlit LCD. It has a feature called LED Motion Plus, which basically strobes the LED backlights. This in turn reduces the amount of motion blur considerably but introduces flicker that some people may be sensitive to.