How much water is too much to drink at once? 1 litre?

Drink to thirst: Recent research has shown that we should drink to thirst, not based on arbitrary amounts like "8 cups a day". So if you are thirsty, drink water, and stop when you feel sated. Someone drinking more than 2-3L of water daily could have an underlying problem and should see a doctor. Drinking too much water can be dangerous and make you very ill (it can cause hyponatremia, coma and death).

Not too much: but it's pushing it. That should be about the maximum size of your stomach. If you are constantly this thirsty, you should perhaps get urine and blood testing to see why it might be. People do get sick from "water intoxication" but usually only if for example they are unconscious and being fed by tube, have a brain tumor (which should cause other symptoms), or are trying to fool a drug test.