Drinking multiple _liters_ of water in a relatively short time can cause water intoxication [1] due to the drop in relative electrolyte levels. I got it once at scout camp where, unfortunately, the medic misdiagnosed me with dehydration and had me drink a gallon of water. I ended up urinating about every ten minutes for the next 24 hours, and is one of the most unpleasant experiences I've gone through.
[1] https://en.wikipedia.org/wiki/Water_intoxication