(covers information from several alternate timelines)
A blood transfusion was the transfer of blood or blood components from one lifeform to another. Compatibility issues between the blood donor and recipient could occur due to differences in antigens or antibodies, specialized proteins used to fight foreign bodies such as viruses or bacteria. It was also likely that interspecies incompatibilities would occur due to more fundamental differences in blood chemistry; for example, Human hemoglobin was iron-based, whereas Vulcan hemoglobin was copper-based.
Bolians were unable to accept direct transfusions from Vulcans; doing so would result in the death of the Bolian. However, there were instances where incompatible blood was altered in order to make a transfusion possible. (VOY: "Prototype")
In 2259 of the alternate reality, Khan Noonien Singh made a bargain with Thomas Harewood to give his ailing daughter Lucille a blood transfusion. Khan's augmented platelets restored Lucille's health, but Harewood did not live to see her recover as the deal entailed he plant a bomb at the Kelvin Memorial Archive. Later, James T. Kirk died of radiation poisoning shortly after the Battle of Luna, but regained consciousness two weeks later after Leonard McCoy gave him a transfusion of Khan's blood. (Star Trek Into Darkness)
In 2371, a Kazon retrieved by the USS Voyager required a complete blood transfusion after his blood cells had bonded with metalic nuclei. The Kazon was later killed on Maje Culluh's orders shortly thereafter, however. (VOY: "State of Flux")