Blood cells are classified into three main types: erythrocytes, leukocytes, and thrombocytes. Erythrocytes are responsible for oxygen transport, leukocytes are involved in immune responses, and thrombocytes play a role in clotting. Leukocytes can be further divided into granulocytes (neutrophils, eosinophils, and basophils) and agranulocytes (lymphocytes and monocytes).