Hi Bob,
Years ago many domestic radios and TVs were the AC/DC type, with one side of the supply cord connected directly to the chassis. Even though they were designed so that there was no exposed metalwork when properly assembled, it was still desirable to ensure that the chassis went to the neutral, just in case a control knob came off or something like that. Some of the cheaper designs also got quite a bit of intermod hum from an AC supply if the chassis went to the hot.
For something like a double-insulated power tool though, it isn't so important, and the motor will run perfectly well from an AC supply connected either way around.
Here in the U.K. quite a big deal is made over correct polarity, but in much of Continental Europe they have non-polarized (or non-keyed) plugs on all portable appliances, even those with grounding type plugs.
