This depends greatly on where you will be going and therefore how available water is. Dehydration is a serious issue, so if in doubt bring a little extra.
For example, if you're going to be hiking in the Arizona desert in summer, figure you're not going to find any water and you have to bring all that you plan to use. Yes, that could be a lot and it will take some space and have some weight. That's part of the price for hiking in a dry area.
Also keep in mind you'll be using more water than usual in the desert. I can go thru a gallon of diluted Gatorade in 2-3 hours under these conditions. The limiting factor of how far I can hike in this case is how much water I'm willing or able to take.
On the other hand, the White Mountains of New Hampshire are quite wet. You will be frequently crossing or going nearby small streams, sometimes crossing larger ones. Except for some areas above treeline, water is quite available.
However, consider that in many places it's not a good idea to drink the water you find directly. Taking less water in a wet area only makes sense if you can process the possibly dirty and infected water that is available.
I have used filters and boiled water, but recently became aware of a newer technology that blasts the buggers in the water with germicidal UV. See, for example, http://www.steripen.com/ultra. By the way, I wrote the firmware that runs that particular unit, although I am not a employee of Hydro-Photon (the manufacturers of the Steri-Pen line).