As question stated.. when should a reverse phase * nice way of sayin reverse polarity I guess * be used on a subwoofer in a car and at home? Whats the benefits really? Other then you switched the wires around during wiring

The idea is to have the sound from the sub hit your ears at the same time as, or closer to the same time as the sound from your mids are hitting your ears. The easiest way to tell which is best is to simply try each setting and see which sounds best, although u may not notice any difference at all.

YUP just like jachin said, it is used to make your sub(*) and your mid-bass hit at the same time. Sometimes you can get more output from your sub(*) (usually if they are not placed right in your car) with in switched one way because it will stop your cross canceling waves.