Patients undergoing orthopedic or heart and blood vessel surgery frequently require blood transfusions both during and after the operation. Patients often have their own blood collected for this purpose over a standard 3- to 4-week period before surgery. A large percentage of patients are not able to pre-deposit their own blood for transfusion. For such patients, an agent that can facilitate self-donation and reduce the need for transfusions from others in less time than the conventional 3 weeks before surgery may improve the overall safety of surgery. This is a randomized, double-blind, placebo-controlled, parallel group, multicenter study to evaluate whether epoetin alfa will enable the self-deposit of at least 4 units of blood in the abbreviated presurgical time period of 2 weeks by patients who are not anemic and who are undergoing orthopedic or heart and blood vessel surgery. The study consists of a 7-day screening period when patients will be tested for eligibility for the study, a 14-day treatment and blood collection period, and a follow-up evaluation period beginning 1 day before surgery and continuing to a study termination visit performed at the patient's discharge from the hospital after surgery. Eligible patients will be randomly assigned to one of four treatment groups: epoetin alfa 300 units/kilogram (U/kg), epoetin alfa 600 U/kg, placebo to match the volume of epoetin alfa 300 U/kg, or placebo to match the volume of epoetin alfa 600 U/kg, given by injection into a vein. Twice as many patients will receive treatment with epoetin alfa as will receive treatment with placebo. A total of 3 doses of study medication will be administered to each patient, one dose given on each of Days 1, 4, and 7 of the study. Additionally, from Day 1 to Day 14 of the study, all patients will receive 200 milligrams of iron and 5 milligrams of a folate supplement daily by mouth to support red blood cell generation. On Day 1, before the first dose of study drug, one unit of blood will be collected from each patient and stored for self-donated blood transfusion. An additional unit of blood will be collected from each patient (before administration of study drug) and stored for self-donated blood transfusion on each of Days 4, 7, 11, and 14, only if the patient's hemoglobin level is \>11.0 g/dL; if a patient's hemoglobin level is \<=11.0 g/dL on any of these days, no blood will be collected on that day, although study drug will be given. A maximum of 5 units of blood will be collected from any patient. If sufficient units for the planned surgery are not collected, preparations will be made for patients to receive needed units of blood from donors. The study duration is 14 days, ending before surgery. Safety evaluations will include laboratory tests, vital signs, and reporting of the incidence of adverse events. Effectiveness will be evaluated by comparing the number of self-donated units of blood collected within 2 weeks, and the change in hemoglobin level among the different treatment groups from before the start of the study to the end of the study. The study hypothesis is that in an abbreviated (2-week) period before surgery, epoetin alfa will facilitate collection of at least 4 units of self-donated blood in patients who are not anemic and who are undergoing orthopedic or heart and blood vessel surgery. Epoetin alfa 300 units/kilogram (U/kg), epoetin alfa 600 U/kg, placebo matching the volume of the 300 U/kg dose, or placebo matching the volume of the 300 U/kg dose, by injection into a vein; given on each of Days 1, 4, and 7 of the study.