Epoetin alfa is an agent similar to a hormone produced in the kidney (ie, erythropoietin) that functions to increase the amount of red blood cells made in the bone marrow. This is a randomized (study drug assigned by chance), open-label (patients and their doctors will know the identity of study drug administered), safety study of 2 dosing regimens (doses and schedules) of epoetin alfa administered to patients with cancer who have chemotherapy-related anemia. Anemia is a lack of red blood cells that can result in symptoms of weakness, shortness of breath, fatigue, tiredness, and decreased activity. The primary outcome measure in the study is the number of patients in each treatment group with at least 1 clinically relevant and objectively confirmed (adjudicated) thrombovascular event (TVE) reviewed by an independent adjudication committee from Day 1 (baseline or the day of the first dose) through Week 16. An external review of relevant clinical data and medical imaging studies by an Adjudication Committee will be performed in a blinded fashion for confirmation of TVEs. The Adjudication Committee will confirm TVEs by reviewing all images (X-ray, Computed tomography \[CT\] scan, ultrasound, Magnetic Resonance Imaging \[MRI\] scan, etc) and other diagnostic procedures auch as coagulation tests or electrocardiograms in combination with a clinical patient profile as described for each specific type of TVE. Only TVEs that are determined by the Adjudication Committee to be clinically relevant and objectively confirmed will be counted in the analysis for the primary endpoint. Approximately 500 patients, who have cancer, are receiving chemotherapy, and are anemic, will take part in the study. Patients will participate in the study for up to 32 weeks (this includes a 2-week screening period to determine eligibility for the study, a 26-week treatment period, and a 4-week follow-up period to have end-of-study assessments \[tests\] performed). The length of participation in the study depends on the length of time the patient is receiving chemotherapy and epoetin alfa; patients in the study may receive up to a maximum of 26 weeks of treatment with epoetin alfa. Patients will be randomly assigned (assigned by chance like flipping a coin) to 1 of 2 treatment groups (Epoetin Alfa QW or Epoetin Alfa TIW). Patients assigned to the Epoetin Alfa QW Group will receive epoetin alfa at an initial dosage of 450 IU/kg once a week and patients assigned to Epoetin Alfa TIW Group will receive epoetin alfa 150 IU/kg 3 times a week by subcutaneous (underneath the skin) injection. Injections will be given preferably on Monday for patients in the Epoetin Alfa QW Group and on Mondays, Wednesdays, and Fridays for patients in the Epoetin Alfa TIW Group. During the study, patients will visit the study center weekly to have a blood sample collected to measure the amount of hemoglobin (red blood cells) in the blood. Depending on the hemoglobin level, the dose of epoetin alfa may be increased or decreased. Regardless of treatment group, if anemia does not improve in patients after 4 weeks of treatment, the dose of epoetin alfa will be increased to 300 IU/kg 3 times a week. If anemia does not improve after 4 weeks at the increased dose level of epoetin alfa (300 IU/kg 3 times a week), treatment with epoetin alfa will be stopped. In addition, during the study, patients may also receive treatment with iron supplements if the level of iron in the blood is low. During the study, safety will be monitored by evaluating adverse events and findings from clinical laboratory tests, 12-lead electrocardiograms (ECGs), blood pressure measurements, and physical examinations. Patients will receive epoetin alfa at an initial dose of 450 IU/kg once a week or 150 IU/kg 3 times a week by subcutaneous injection, preferably in the abdomen, for up to 4 weeks after the last dose of chemotherapy for a maximum of 26 weeks. Injections for Epoetin Alfa QW Group will be at the study center and for Epoetin TIW Group, the 1st weekly injection will be at the study center and the 2nd and 3rd weekly injections will be at the study center or at home by self-administration.