Yes, too much water is dangerous, you can suffer from Water Intoxication, and to a related problem resulting from the dilution of sodium in the body, hyponatremia.
It's Not How Much You Drink, It's How Fast You Drink It
A healthy adult can process 15 liters of water a day! You are unlikely to suffer from water intoxication, even if you drink a lot of water, as long as you drink over time as opposed to intaking an enormous volume at one time. As a general guideline, most adults need about three quarts of fluid each day. Much of that water comes from food, so 8-12 eight ounce glasses a day is a common recommended intake. You may need more water if the weather is very warm or very dry, if you are exercising, or if you are taking certain medications. The bottom line is this: it's possible to drink too much water, but unless you are running a marathon or an infant, water intoxication is a very uncommon condition.
Hope this helps!