There are virtually no negative side-effects to drinking green tea, even if you drink a gallon of it per day. The only thing that it can do in high amounts is inhibit your body’s ability to absorb iron and folic acid. For most people, the risk here is negligible. Only women who are pregnant or trying to get pregnant are advised to hold back, and even then the recommendation is to limit oneself to one or two cups per day. Moreover, the problem can be completely negated with a vitamin supplement.
That said, the optimal amount seems to be around seven cups, and there is no real benefit to drinking more than 10 cups of green tea in a day. It’s just the law of diminishing returns: eventually, your system just won’t process the catechins as efficiently (note: the mechanism by which green tea provides health benefits is unclear at present; I cite the catechins because they are what most researchers suspect to be responsible). So if you can manage seven cups without intestinal discomfort, there’s no reason to go for more.
Finally, I agree with the answers above that green tea is ultimately nothing more than a supplement. It can help you lose weight, but it won’t lose weight for you. So while seven cups may be optimal for health benefits (including those that go beyond weight loss), this does not mean that you should feel pressured to drink that much. Other factors—such as overall diet and exercise—are more important than whether you had three cups or 30 cups of green tea.
P.S. My answer has been informed in part by this study.