Yes, you can. From Chemistry.com (http://chemistry.about.com/cs/5/f/blwaterintox.htm
Question: Can You Drink Too Much Water?
Answer: You've probably heard that it's important to 'drink plenty of fluids' or simply 'drink lots of water'. There are excellent reasons for drinking water, but have you ever wondered if it's possible to drink too much water. Here's what you need to know:
Can You Really Drink Too Much Water?
In a word, yes. Drinking too much water can lead to a condition known as water intoxication and to a related problem resulting from the dilution of sodium in the body, hyponatremia. Water intoxication is most commonly seen in infants under six months of age and sometimes in athletes. A baby can get water intoxication as a result of drinking several bottles of water a day or from drinking infant formula that has been diluted too much. Athletes can also suffer from water intoxication. Athletes sweat heavily, losing both water and electrolytes. Water intoxication and hyponatremia result when a dehydrated person drinks too much water without the accompanying electrolytes.
What Happens During Water Intoxication?
When too much water enters the body's cells, the tissues swell with the excess fluid. Your cells maintain a specific concentration gradient, so excess water outside the cells (the serum) draws sodium from within the cells out into the serum in an attempt to re-establish the necessary concentration. As more water accumulates, the serum sodium concentration drops -- a condition known as hyponatremia. The other way cells try to regain the electrolyte balance is for water outside the cells to rush into the cells via osmosis. The movement of water across a semipermeable membrane from higher to lower concentration is called osmosis. Although electrolytes are more concentrated inside the cells than outside, the water outside the cells is 'more concentrated' or 'less dilute' since it contains fewer electrolytes. Both electrolytes and water move across the cell membrane in an effort to balance concentration. Theoretically, cells could swell to the point of bursting.
From the cell's point of view, water intoxication produces the same effects as would result from drowning in fresh water. Electrolyte imbalance and tissue swelling can cause an irregular heartbeat, allow fluid to enter the lungs, and may cause fluttering eyelids. Swelling puts pressure on the brain and nerves, which can cause behaviors resembling alcohol intoxication. Swelling of brain tissues can cause seizures, coma and ultimately death unless water intake is restricted and a hypertonic saline (salt) solution is administered. If treatment is given before tissue swelling causes too much cellular damage, then a complete recovery can be expected within a few days.
It's Not How Much You Drink, It's How Fast You Drink It!
The kidneys of a healthy adult can process fifteen 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.