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, double-blind, placebo-controlled multicenter study to compare the ability of epoetin alfa and placebo in reducing or preventing anemia and transfusions, and to investigate quality-of-life benefits associated with the use of epoetin alfa in patients receiving chemotherapy for selected cancers. During the double-blind period there will be two groups of patients: one group receiving epoetin injections under the skin 3 times per week (starting at 150 units per kilogram, adjusted if needed to a maximum of 300 units per kilogram) and other group receiving injections under the skin of a placebo of matching appearance and volume. If hemoglobin rises above 140 grams per liter (women) or 150 grams per liter (men), the dose will be adjusted to keep hemoglobin within a target range. A 12-week open-label extension of the study will be available to all patients completing the 12-week comparison period. The primary measure of effectiveness is determined by the proportion of patients with no transfusions after the first month. Additional measures of effectiveness include: the proportion of responders, the change of hemoglobin unrelated to transfusion, cumulative transfusion rate and proportion of patients transfused during the double-blind phase (excluding the first month), as well as the mean change over the study period in scores for energy, activity and overall quality of life. The results will be analyzed separately for non-platinum-containing chemotherapy and for different tumor types. Safety evaluations include assessments of the incidence and severity of adverse events, clinical laboratory tests, vital sign measurements, and physical examinations. The hypothesis of the study is that epoetin alfa is superior to placebo in improving anemia, reducing the number of transfusions, and improving quality of life. Epoetin alfa 150 units (U) per kilogram (kg) or placebo, 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 (12 weeks): dose to maintain target hemoglobin range.