Reverse polarity is something that is real, but not "reverse negative polarity"
If there is voltage to ground somewhere usually it trips a circuit breaker in the panel. But if the amps are low enough or the CB is bad you have a dangerous situation as mentioned above. Usually fire. GFCI's will trip and you will get shocks too.
How old is the house? Most appliances will work fine if the hot and neutral are switched around.