Red blood cells (erythrocytes, RBCs for short) are really important - they carry the oxygen all your cells need to survive (as they do for other air-breathing organisms). They are red from hemoglobin, which when bound with oxygen turns red. If someone doesn't produce any RBCs, they will die without a blood transfusion and treatment. I do not know of a disease where no RBCs are produced, however, there are diseases that cause low RBC production (none marrow disorders) or abnormal hemoglobin (iron deficiencies).