Fresh or processed berries are considered to be beneficial for health by many consumers. Fruits of closely related species of plants sometimes possess strikingly different phytochemistry and biological activities. Therefore, even though similar research has been conducted on a number of Rubus berries, there is much relevance associated with the investigation of species that have not been previously studied. In the current report, the fruits of three wild Jamaica-grown species: Rubus jamaicensis, Rubus rosifolius and Rubus racemosus, and of the Michigan-grown Rubus acuminatus, Rubus idaeus cv. Heritage and Rubus idaeus cv. Golden were analyzed for their anthocyanin contents, and lipid peroxidation, cyclooxygenase enzyme and human tumor cell proliferation inhibitory activities. It was revealed that the fruits contained superior levels of anthocyanins (146–2199 mg/100 g fresh weight) to those previously reported for other raspberry and blackberry species, and their hexane, EtOAc and MeOH extracts showed good antioxidant activity, the majority of the extracts exhibiting over 50% lipid peroxidation inhibitory activity at 50 μg/mL. The hexane extracts of the Jamaican Rubus spp. demonstrated moderate COX inhibitory activity (27.5–33.1%) at 100 μg/mL, and exhibited the greatest potential to inhibit cancer cell growth, inhibiting colon, breast, lung, and gastric human tumor cells by 50, 24, 54 and 37%, respectively. The high anthocyanin content and biological activities of these fruits indicate that their consumption would be beneficial to health, and that they may be useful in the production of functional foods containing an efficacious dose of anthocyanins.