will a hydrogen economy deplete the world's water resources?

Absolutely not. 
It will just add another, small, side loop to the water cycle.

water cycle:
http://www.kidzone.ws/water/
http://ga.water.usgs.gov/edu/watercyclehi.html

In hydrogen economy fuel (hydrogen) is made from water.
When fuel is burned (e.g. in car) the same amount water is re-created.
It evaporates and joins other water in the atmosphere.
Eventually, the water vapor precipitates and water rains back to the Earth.
http://auto.howstuffworks.com/hydrogen-economy.htm


It - hydrogen economy - has some benefits over use of gasoline in cars
http://auto.howstuffworks.com/hydrogen-economy.htm

However, one needs to keep on mind that it does not create energy.
To make hydrogen from water takes energy. Hydrogen is a carrier,
similar to a battery or a transmission line, not a source.

For new sources, to replace  current fossil fuels we have very few options :
some renewable sources, such as tides, eg
http://www.baycrossings.com/Archives/2002/09_October/tidal_energy.htm

but mostly SPS and fusion. Both are being pursued:

SPS
http://www.space.com/businesstechnology/technology/solar_power_sats_011017-1.html

Fusion
http://fusedweb.pppl.gov/

Both of these method are feasible in the near future - but require
additional research, The more we invest - the sooner they will be
available.

Considering the problems and escalating cost of securing Middle East
oil for use in the US and other industrialised nations
http://costofwar.com/
it was suggested that it may be better to invest the current resources into
the research which would allow  exploitation of these new technologies
rather then of mineral resources found in the developing world.

Either source of energy, fossil, nuclear or solar, has to be combined with
the hydrogen technology to produce an sustainable, pollution free
future for our children.

Hedgie

That and the comments fully answer my question

The combustion of hydrogen in air produces water as the reaction product:

2*H2 + O2 -> 2H2O + energy

If we ultimately end up producing hydrogen fuels by the electrolysis
of water (i.e., splitting H2O into H2 and 1/2O2, see
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/electrol.html), then
the burning of hydrogen will simply regenerate the original water.  If
we obtain hydrogen by steam reforming of natural gas followed by a
water-shift reaction (net reaction: CH4 + 2*H2O -> CO2 + 4*H2, see
http://www.sasked.gov.sk.ca/docs/chemistry/mission2mars/contents/chapter4/steamreform.htm),
then we will actually increase (slightly) the total amount of water
present on Earth.  (We will be "undoing" what the combined effects of
ancient photosynthesis and burial of organic matter did over geologic
time by remaking the CO2 and H2O that originally when into making the
methane).

If, as is likely, the fuel generation, transportation, and fueling
system of a future hydrogen economy is not "perfect", and ends up
leaking some hydrogen into the atmosphere, that hydrogen could
potentially be lost from the Earth via the mechanisms of Jeans
(thermal) escape (http://www.cs.trinity.edu/~mlewis/PlAtm/Jeans.html)
and solar-wind-induced ablation/stripping of the upper atmosphere.
These processes that deplete the Earth's atmosphere in hydrogen have
been going on since the atmosphere first formed. If we got the
hydrogen from splitting water, this would, very very slightly, enhance
the natural depletion of the Earth of water.   The rate at which the
Earth is being depleted in water because of this is left as an
excercise to the reader (hint, see
http://witcombe.sbc.edu/water/physicsearth.html)

I wouldn't worry about the water supply.  Until we are able to produce
more electricity in a better way, a hydrogen economy would deplete our
fossil fuel supply because we need power to get hydrogen out of water.
 Of course, if we were to replace all of our petroleum vehicles with
hydrogen vehicles tomorrow, the hydrogen supply itself could be
considered relatively depleted so the concern over water seems
premature.