The World Health Organization WHO has codes for doctors to use when diagnosing them. Their total amount of codes are 14,199, but I think there are more diseases being discovered all the time, and I think there are many illnesses, especially rare or exotic ones, that the WHO has not classified yet. ICD means International Classification of Diseases. The latest book of those codes is version #10.
There are 12,420 codes in ICD-10 (14,199 with the fourth-character place of occurrence codes in Chapter XX (External Causes of Morbidity and Mortality).