Cancer patients often experience anemia due to the disease itself, chemotherapy or both. Quality of life is also affected, in part because of the fatigue associated with anemia. Previous studies with epoetin alfa have suggested that achieving a higher hemoglobin level may improve quality of life and help patients live longer. This study is a 12-week randomized, double-blind, placebo-controlled, multicenter study (with an open-label extension) to assess the effectiveness of treatment with epoetin alfa in reducing the need for red cell transfusion by improving anemia in patients with multiple myeloma whose hemoglobin is less than 11 grams per deciliter. There will be 4 groups of patients in the study. Patients will first be placed into 2 groups according to whether or not they received at least 1 blood transfusion within the previous 3 months. Within each of these 2 groups, patients will then be randomly assigned to receive either epoetin alfa or placebo for 12 weeks. Dosing is initiated at 150 units per kilogram (U/kg) injected under the skin 3 times weekly for 4 weeks, then either continued at 150 U/kg or adjusted to 300 U/kg according to hemoglobin levels for the remaining 8 weeks. All patients who complete the 12-week double-blind period will be eligible to continue receiving epoetin alfa for an additional 12 weeks in an open-label extension of the study. The primary measures of effectiveness will be determined by the number of units of blood transfused, the proportion of patients requiring transfusion, and the number of units transfused relative to whether or not they received transfusions before the study. Additional effectiveness measures include the number of patients whose hemoglobin level reach at least 12 grams per deciliter (anemia considered "corrected") or who have an increase in hemoglobin of at least 2 grams per deciliter, and the change in the percentage of red blood cells and number of developing red blood cells in the blood. Changes in quality-of-life (Nottingham and visual analog scale) and performance scores will also be measured. Safety evaluations (incidence of adverse events, laboratory tests, and vital signs) and changes in underlying multiple myeloma will be assessed. The hypothesis of the study is that epoetin alfa will be superior to placebo in reducing the need for transfusions and improving anemia and quality of life. Double-blind: Epoetin alfa 150 units per kilogram (U/kg) injected under the skin 3 times weekly for 4 weeks; then either continued at 150 U/kg or adjusted to 300 U/kg according to hemoglobin levels for the remaining 8 weeks. Open-label: dose to maintain target hemoglobin range.