There are as many answers to this question as there are researchers investigating the natural properties of green tea. For example, Herbs for Health magazine cites a Japanese report stating that men who drank ten cups of green tea per day stayed cancer-free for three years longer than men who drank less than three cups a day (there are approximately 240 - 320 mg of polyphenols in three cups of green tea). Meanwhile, a study by Cleveland's Western Reserve University concluded that drinking four or more cups of green tea per day could help prevent rheumatoid arthritis, or reduce symptoms in individuals already suffering from the disease.  And Japanese scientists at the Saitama Cancer Research Institute discovered that there were fewer recurrances of breast cancer, and the disease spread less quickly, in women with a history of drinking five cups or more of green tea daily.  

It gets more confusing.  A University of California study on the cancer-preventative qualities of green tea concluded that you could probably attain the desired level of polyphenols by drinking merely two cups per day.  On the other hand, a company selling a green tea capsule formula insists that ten cups per day are necessary to reap the maximum benefits.
How can you make sense of these conflicting claims? Given all the evidence, it is probably safe to plan on drinking four to five cups of green tea per daily. If you're a real devotee, by all means drink more; but whether or not you'll derive added health benefits remains to be determined by further research.  

Other Benefits

New evidence is emerging that green tea can even help dieters.   In November, 1999, the American Journal of Clinical Nutrition published the results of a study at the University of Geneva in Switzerland.  Researchers found that men who were given a combination of caffeine and green tea extract burned more calories than those given only caffeine or a placebo.
Green tea can even help prevent tooth decay! Just as its bacteria-destroying abilities can help prevent food poisoning, it can also kill the bacteria that causes dental plaque. Meanwhile, skin preparations containing green tea - from deodorants to creams - are starting to appear on the market.

Harmful Effects? 
To date, the only negative side effect reported from drinking green tea is insomnia due to the fact that it contains caffeine.   However, green tea contains less caffeine than coffee: there are approximately thirty to sixty mg. of caffeine in six - eight ounces of tea, compared to over one-hundred mg. in eight ounces of coffee.