You can drink too much water, which is called water intoxication. Water intoxication results when a dehydrated person drinks too much water without the accompanying electrolytes. You usually need to drink a large volume of water in a very short period of time to be in danger of this, which is why it's not common. It causes the sodium levels in the blood to drop. The excess water causes dilution. This disturbs the water balance in the brain and can cause seizures and even death.
You can safely drink up to 10 liters of water a day though, unless you have a kidney disease and are to limit fluids.