There do seem to be some health benefits from drinking green tea, but the results are not conclusive.
Wikipedia has an informative page about green tea. It would seem that it can have a beneficial effect on cholesterol levels and there have been some studies that link it to weight loss. Like any tea, it does contain some caffeine.
The term "green tea" doesn't refer to a particular type of tea, but to the length of time that the tea leaves are oxidized before processing. White tea is oxidized for the least time, then green tea, then oolong, then black tea.
So if you like it, then drink it. It contributes towards your overall liquid intake, it has no calories, helps to fill you up, and while you are drinking it you can't be eating or drinking anything else!!
I recently discovered Tick Tock rooibos green tea. This is the "red bush" tea which you will know if you have read the No 1 Ladies Detective Agency books. It is really delicious. You can get it in Waitrose - possibly other supermarkets too.