(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. After James T. Kirk died of radiation poisoning later that year, Doctor Leonard McCoy conducted a transfusion from Khan Noonien Singh to Kirk, as Khan's blood had been discovered to have regenerative qualities. McCoy managed to resurrect Kirk by creating a serum from Khan's blood, though the effects of the transfusion left Kirk unconscious for two weeks. (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. Seska claimed that she had a childhood disease, Orkett's disease, which infected her blood, and was warned to never donate blood for transfusion. This was a ruse to try to avoid providing a blood sample for the files of Voyager, which would have revealed that she was Cardassian and not Bajoran as she claimed. (VOY: "State of Flux")