A water main burst in winter
Contamination at the source or processing plant
Prolonged power outage
Weather Events: Hurricane, blizzard, etc.
It is recommended (source: FEMA) to store at least one gallon per person per day, and have 2 weeks worth of water on hand. This will allow you to ride out disruptions of your running water supply. If you can't store two weeks worth, store as much as you can.
While storing as much water as possible is optimal, water takes up a lot of space and can get heavy in large volumes. Your water plan should include storage water but also water filters or treatment methods to clean contaminated water.