Are blackberries good for you? Well they do have high amounts of antioxidants in the form of phenolic compounds: anthocyanins (the dark pigments), tannins, ellagic acid, ellagitannins, gallic acid, quercetin (which is often studied for its anti-inflammatory properties) and cyanidins. So yes, they are quite good for your health.
ORAC Source
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010