One quart in mild weather.
One and a half quarts backpacking in mild weather
5 quarts in desert hiking

For a short hike in mild weather I carry a 40oz stainless steel bottle. If I expect to be out longer I will carry two bottles or a bottle and a hydration bladder. What can I say- I drink a lot of water!

It does not only depend on the region it also depends on the weather conditions. For me the variation is not a little but almost a magnitude of ten even in the same region. In cold, humid weather conditions one quart is plenty. In hot weather and probably carrying some gear it may easily be 5qts to 7 qts. Lots of altitude changes easily add 1 qt for the higher intensity.
The amount also depends on whether I will have a reliable source for refills along the way.
I prefer the Platypus bladders as the are really easy to clean and dry.
A motorcycle tour in full protective gear on a hot summer day may require 10+qts.

Summer hikes in Texas I'll load up with a minimum of 4 liters of water plus one bottle of sport's drink. I ran out of water once on a trail down here and it was really scary. Since then I always take too much water to make sure I'll have enough.
-Blast

It's always difficult to figure how much water is enough. It would be easier if water weighed less.

same thing happened to me and now i always take too much. which is just right.

Isn't that the truth. It effectively weighs less if it is in you. Always a good idea to super-hydrate before you hit the trail. That way you don't have to carry it on your back. Even then I carry a 100oz bladder and an extra liter Nalgene for cooking with.

If I'm out for the day, I'll bring along a 100oz/3L camelbak.

From 1 to 4 liters depending on conditions. In the desert with highs in 80's maybe more.

I would expect to carry a gallon of water per day in the desert BUT I've never hiked through a desert either.