Cancer patients often experience anemia due to the disease itself, chemotherapy, or both. Quality of life is also affected, due in part to the tiredness associated with anemia. Previous studies with epoetin alfa have suggested that epoetin alfa increases hemoglobin and reduces the incidence of red blood cell transfusions and that achieving a higher hemoglobin level may improve quality of life. This is a randomized, open-label, multicenter study that evaluates the effects of early treatment with epoetin alfa compared with standard anemia care alone to determine its impact on the need for blood transfusions, tumor response, anemia and quality of life, as well as on the safety of epoetin alfa when used in the prevention of anemia during chemotherapy in adult patients with cancer. Patients will receive epoetin alfa injections (10,000 units) under the skin 3 times a week until 4 weeks after the last day of the last chemotherapy cycle, in addition to best standard care, or best standard care alone. Best standard care during chemotherapy may include red blood cell transfusions, white cell growth factors, and iron supplementation, as needed. The dose of epoetin alfa may be adjusted up (to 20,000 units) or down (to 75% of the last dose) based on hemoglobin level.