Is there a reasonable relationship between the volume of cooling water
a power plant requires and the megawatts of power produced. 
Especially for once-through cooling plants, I would like enough data
to find a relationship such that if I know the size of the plant in
megawatts (MW) I can estimate (roughly) the volume of water withdrawn
for cooling in millions of gallons per day.

Not an answer, but maybe a couple of pointers.
If you know the plant efficiency, you can estimate the amout of
"waste" heat produced.  If, for example, a  plant is 10% efficient
(I've no idea if this figure is realistic), then for every W of
electricity produced, 9W of heat must be dissipated.

Now - a W is one joule/second, or 86.4 kJ/day.
4.184 J is sufficient energy to raise 1 ml of water by 1 degree C,
so...
over the course of a day, our 86.4 kJ could heat 20.65 l of water by 1
degree.

Using this logic, knowing the plant size, and estimating the
efficiency and the temperature differential between intake and
discharge, you can calculate the amount of water required to carry
away the "waste" energy.