A blood count was a medical test run to determine the number of each component cell type in blood.
In 2155, the Human-Vulcan hybrid Elizabeth had an elevated white blood cell count. (ENT: "Terra Prime")
After encountering the dikironium cloud creature in 2268, Ensign Rizzo's blood count was 60% less than normal. (TOS: "Obsession")
In 2269, while trapped inside Janice Lester's body, James T. Kirk noted that "his" pulse, blood pressure, and blood count were all normal and wondered why "he" was in sickbay. Later, "Kirk"'s blood count was determined by Doctor Leonard McCoy to be normal while Lester was inhabiting his body. (TOS: "Turnabout Intruder")
While acting as a temporary host for a Trill symbiont in 2367, William T. Riker's white blood cell count was elevated as his body rejected the foreign entity. (TNG: "The Host")
In 2372, Ekoria relayed a message from Jadzia Dax to Julian Bashir that Epran's white blood count was up 12%, a good sign, according to Bashir. (DS9: "The Quickening")