I led extended backpacking trips in Grand Canyon country for several years, and we required everyone carry at MINIMUM a gallon (almost 4 litre) per person per day -- which adds up. (Though rarely did we plan trips that did not have dependable water sources within a day's walk, meaning we would start and end the day with bellies full of water.)
Different people consume (and lose) at different rates, so the above would usually balance out in a group.
Addendum: As some have pointed out, there are varying recommendations, and even Grand Canyon National Park seems to have some difference of opinion: exhibit A, and exhibit B
Considerations such as difficulty of the terrain, whether there will be a water-source where you are going, whether you start the hike well-hydrated, what time of day you are hiking, etc all play into it. As does the consideration of more water = more weight = more energy expended = more water needed. For some people, adding 2 gallons (7.6 litre) to their pack would make it difficult for them to go anywhere...
In short, if you think you need more, take more. Cache water (if possible). Be smart. Know your limits.