I'd like an estimate for the total number of fire hydrants in the U.S.

I had expected this search to be more clear-cut than it turned out to
be. Although most cities keep records of how many fire hydrants they
have, there does not seem to be a national databank for this type of
information.

A company called Mueller Water Products is said to be the source of
about half the fire hydrants in the United States, and multiple online
sources (including Mueller's own website) say that Mueller maintains
three million fire hydrants. From this, it can be estimated that there
are approximately 6 million fire hydrants in the US.

"You cannot turn on your water faucet, go roller skating, get a drink
at a public fountain, or drive your car without thinking about
Hieronymus Mueller. In 1857, Mueller opened a gun repair shop on
Decatur's West Main Street, and this grew into a national company that
still makes fire hydrants (by now, about half of all fire hydrants in
the US have been made by the Mueller company) and related 'flow
control' equipment."

Heritage Network: Hieronymus Mueller Museum
http://faculty.millikin.edu/~kborei.library.mu/Hn/details.html 

"Nearly half of all the fire hydrants in the nation are made in
Decatur by the Mueller Corporation."

Decatur & Macon County Living: Did you know?
http://www.welikeithere.com/didyouknow/didyouknow1.php

"Mueller CO. considers a fire hydrant to be a critical piece of
emergency equipment used to preserve lives and property. For this
reason all Mueller Fire Hydrants are designed, built and tested to
assure high performance and dependability. All of our Hydrants come
with a 10 YEAR LIMITED WARRANTY ON PARTS AND WORKMANSHIP for the
Mueller Super Centurion® Fire Hydrant. The claim of outstanding and
reliability is proven by the fact that nearly half of all fire
hydrants sold in the US today are manufactured by MUELLER CO."

Marshall J. Brown Company, Inc.: Fire Protection
http://www.mjbco.com/fireprotect.html

"Mueller Water Products is a leading North American manufacturer of a
broad range of water infrastructure and flow control products for use
in water distribution networks, water and wastewater treatment
facilities, gas distribution systems and fire protection piping
systems. We believe we have the most comprehensive water
infrastructure and flow control product line in our industry and enjoy
leading market positions based on the estimated market share of our
key products, broad brand recognition and a strong reputation for
quality and service within the markets we serve. We maintain one of
the largest installed bases of products in the United States,
including approximately three million fire hydrants and approximately
nine million iron gate valves. Our products are specified for use in
all of the top fifty metropolitan areas in the United States."

Mueller Water Products, Inc.: Corporate
http://www.muellerwaterproducts.com/corp/corp.html

I found one source which claims that there are "tens of millions of
fire hydrants in the United States," but no backup data is provided,
so I'd take this with the proverbial grain of salt:

"However, there are tens of millions of fire hydrants in the United
States, every one ostensibly a useful tool to protect us."

Backflow Prevention TechZone
http://www.backflowpreventiontechzone.com

My Google search strategy:

Google Web Search: "million fire hydrants"
://www.google.com/search?hl=en&q=%22million+fire+hydrants%22

Google Web Search: "1000000..20000000 fire hydrants"
://www.google.com/search?hl=en&q=%221000000..20000000+fire+hydrants%22

Google Web Search: estimate OR estimated OR approximately "fire
hydrants" "united states"
://www.google.com/search?hl=en&q=estimate+OR+estimated+OR+approximately+%22fire+hydrants%22+%22united+states%22

I hope this is helpful. If anything is unclear or incomplete, or if a
link does't work for you, please request clarification; I'll be glad
to offer further assistance before you rate my answer.

Best regards,
pinkfreud

Thanks for your help!  This provides the info I need.