How deep does the water need to be for a professional high-diver to
safely dive into it?   Specifically, how deep is the water in the Las
Vegas Bellagio "O" show pool when the vertically-adjustable bottom is
set at its lowest for the high-diving part of the show?  What is the
depth of the typical Olympic diving pool?

Hi

according to the Cirque du Soleil website the depth of the Bellagio O pool is 25ft:
http://www.cirquedusoleil.com/CirqueDuSoleil/en/pressroom_old/prinfo/backgrds/shows/residents/O.htm
from an article in the NY Times:
"For dives from the 60-foot tower, the relevant sections sink to their
maximum depth of 25 feet."
http://query.nytimes.com/gst/fullpage.html?res=9C02E5DD1E3EF931A25751C1A96F958260&pagewanted=print

The Fédération Internationale de Natation Amateur (FINA, International
Federation of Amateur Swimming) also serves as the governing body for
Olympic Diving. Their requirements for diving facilities can be found
here:
http://www.fina.org/rules/FR/pics/rules_fr_dim.pdf

I saw Elmer Fudd do it into a glass of water from 100 feet.