A 2006 study, published in the Journal of the American Medical Association, found that :

Green tea consumption is associated with reduced mortality due to all causes and due to cardiovascular disease but not with reduced mortality due to cancer."

Source

Another, published in Arteriosclerosis, Thrombosis, and Vascular Biology (2010) claimed :

High tea consumption is associated with a reduced risk of CHD [Coronary Heart Disease] mortality. Our results suggest a slight risk reduction for CHD mortality with moderate coffee consumption and strengthen the evidence on the lower risk of CHD with coffee and tea consumption."

Source

Neither study was able to pinpoint the active ingredients that would lead to such effects.

Research from Charité Universitäts, Berlin, examined the hypothesis that tea might help alleviate cardiovascular problems by acting as a vaso-dilator (i.e. a blood vessel relaxant). But no firm results were able to pinpoint which chemical components were leading to tea's apparent benefits.

Consumption of tea is associated with reduced progression of atherosclerosis and lower cardiovascular mortality, However, the substance(s) mediating the favorable cardiovascular effects of tea in vivo have not yet been identified."

See: Tea-induced improvement of endothelial function in humans: No role for epigallocatechin gallate (EGCG)

Note: the article above gives links to numerous other studies claiming a wide range of medical benefits for tea drinking.