Water doesn't go bad, but it can get a bad taste or odor. It can also grow bacteria which can be in the air, on your hands or in the container.
Municipally treated tap water contains chlorine which is a disinfectant. If you store for emergency, it is unlikely that some chlorine will make much of a difference. PUR filter is a carbon filter, which will remove chlorine. Non-chlorinated water is much more prone to bacteria growth than chlorinated, so for emergencies and long-term storage I would probably not filter it.