The San Francisco Public Utilities Commission is responsible for the storage, quality control and distribution of the area's drinking water.
SF has an emergency water supply for use in emergencies with a specific focus on providing water after a potential major earthquake. The main source of damage after the 1906 earthquake was fire, so this is something that has been a priority for disaster preparedness. The water supply does get used occasionally - for example, it was used in the March 2014 Mission Bay fire. However, it turns out there are huge deficiencies in the emergency water supply: "The Fire Department has enough emergency resources to battle three big fires like the one this month that destroyed a Mission Bay apartment building under construction. But if more fires than that break out in areas with no access to the backup water supply system - a fearsome likelihood in the aftermath of a major earthquake - there probably won't be enough emergency equipment to put them all out."
Water if there's a major earthquake
Check out this excellent map of fire hydrants around the city that have been hooked up to sources of potable water. If you invest in a hydrant wrench, you can drink water from these hydrants in an emergency. The map was made by Scott Kildall. [source]
Auxiliary Water Supply System (AWSS)