We often hear the advice to drink 8 glasses of water each day.
What evidence is there for this recommendation, and how was that amount determined?
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There is no evidence.
If you're interested in some historical background about this recommendation, there is interesting quote from "Medical myhts" (2007) article in British Medical Journal:
The advice to drink at least eight glasses of water a day can be found throughout the popular press. One origin may be a 1945 recommendation that stated: A suitable allowance of water for adults is 2.5 litres daily in most instances. An ordinary standard for diverse persons is 1 millilitre for each calorie of food. Most of this quantity is contained in prepared foods. If the last, crucial sentence is ignored, the statement could be interpreted as instruction to drink eight glasses of water a day.
Another endorsement may have come from a prominent nutritionist, Frederick Stare, who once recommended, without references, the consumption “around 6 to 8 glasses per 24 hours,” which could be “in the form of coffee, tea, milk, soft drinks, beer, etc.” The complete lack of evidence supporting the recommendation to drink six to eight glasses of water a day is exhaustively catalogued in an invited review by Heinz Valtin in the American Journal of Physiology. Furthermore, existing studies suggest that adequate fluid intake is usually met through typical daily consumption of juice, milk, and even caffeinated drinks. In contrast, drinking excess amounts of water can be dangerous, resulting in water intoxication, hyponatraemia, and even death.
The review referenced above is "Drink at least eight glasses of water a day." Really? Is there scientific evidence for "8 x 8"? (2002) by Heinz Valtin. But if you just want single answer, then:
No scientific studies were found (...).
Some researchers are trying to determine recommended total daily fluid intake, you can search PubMed if you like. Some sample articles from past few years:
To drink 8 cups (2 liters) of water per day should not be considered a recommendation but an estimation of the average water needs for sedentary adults living in moderate climates (who sweat only a little).
There is not possible to provide the evidence about "how much everyone needs to drink per day" because everyone needs different amount every day. You need to drink as much water as you lose it from your body, mainly by urinating and sweating. This is probably at least 1 liter per day, but if you sweat a lot, you may need 5 or more liters per day.
The Institute of Medicine in the US has determined the Adequate Intake (AI) of water, which is 3.7 liters for young men and 2.7 liters for young women. This does not mean you need to drink that much, but that 98% of young men and women (including more active and hence sweating more) will not need more than 3.7 or 2.7 liters per day.