The primary measure of effectiveness will be determined by the number of patients who receive an allogenic red blood cell transfusion during the study and during each chemotherapy cycle. Additional measures of effectiveness include: the average number of units transfused during each cycle, change in quality of life (feeling of well-being, as assessed by responses to 3 different patient questionnaires), change in hemoglobin level, relationship between change in hemoglobin and quality of life, tumor response, and the number of patients surviving up to 12 months after the end of treatment. Safety evaluations (incidence of adverse events, clinical laboratory tests, vital signs, and physical examinations) will be performed throughout the study. The study hypothesis is that treatment with epoetin alfa will reduce the need for red blood cell transfusions, increase hemoglobin levels, improve quality of life, and result in a positive tumor response in patients with cancer who are receiving chemotherapy. This study will be conducted in the Netherlands and will only enroll European patients. 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, or best standard care. Dose may be adjusted up (to 20,000 units) or down (to 75% of the last dose) based on hemoglobin level.