The amount of water you should carry depends heavily on outdoor temperatures and varies from person to person, but the rule of thumb is: drink 1/2 to 1 quart of water per hour of hiking. On a hot day climbing up a mountain, your body can lose 1 - 2 quarts per hour from perspiration. It's pretty simple though, if you feel thirsty at all, drink.
If you want to take it one step futher, you can determine how much water you are losing during exercise. Weigh yourself before and after a hike or workout. Subtract about 7% from the difference in pounds (to account for the burned calories), then multiply by 16. That's more or less how many ounces of water you need to replace.