Like everyone else said, it depends, but most people often carry more then they need.

I typically carry 40 oz max, two 20 oz soda bottles. That's a bit over 2 pounds leaving a water source. It takes time to get water, so even when the sources are fairly frequent you want to carry enough so you don't have to stop at each one, but not so much your lugging extra weight for no good reason.

At some shelter sites, water sources can be quite a distance from the trail, and steeply down hill. Therefore it's a good idea to be able to carry at least one gallon of water so you only need to make that trip down to the spring once. I use a silnylon water bag which holds a gallon, weights next to nothing and takes up no space in the pack.