Inclusion Criteria: - Patients up to 65 years of age at time of registration with a diagnosis of SAA; SAA is defined as follows: 1. Bone marrow cellularity less than 25% or marrow cellularity less than 50% but with less than 30% residual hematopoietic cells 2. Two out of three of the following (in peripheral blood): neutrophils less than 0.5 x 10^9/L; reticulocytes less than 20 x 10^9/L - Patient must have an available unrelated donor with a 7/8 or 8/8 match for HLA-A, B, C, and DRB1 antigen; typing is by DNA techniques: intermediate resolution for A, B, and C, and high resolution for DRB1; HLA-DQ typing is recommended but will not count in the match - Patient and/or legal guardian able to provide signed informed consent - Matched unrelated donor must consent to provide a marrow allograft - Patients with adequate organ function as measured by: 1. Cardiac: left ventricular ejection fraction at rest must be greater than 40% or shortening fraction greater than 20% 2. Hepatic: serum bilirubin less than 2x upper limit of normal for age as per local laboratory) (with the exception of isolated hyperbilirubinemia due to Gilbert's syndrome), ALT and AST less than 4x upper limit of normal for age (as per local laboratory) 3. Renal: serum creatinine less than 2x upper limit of normal for age (as per local laboratory) 4. Pulmonary: FEVl, FVC, and DLCO (corrected for Hb) greater than 50% predicted; for patients in which pulse oxymetry is performed, O2 saturation greater than 92% - Diagnosis of Fanconi anemia must be excluded in patients younger than 18 years of age by diepoxybutane testing on peripheral bloor or comparable testing on marrow. Exclusion Criteria: - Clonal cytogenetic abnormalities associated with MDS or AML on marrow examination - Diagnosis of other "congenital" aplastic anemias such as: Diamond-Blackfan; Shwachmann-Diamond; congenital amegakaryocytosis - Symptomatic or uncontrolled cardiac failure or coronary artery disease - Karnofsky performance status less than 60% or Lansky less than 40% for patients younger than 16 years old - Uncontrolled bacterial, viral or fungal infections (currently taking medication and progression of clinical symptoms) - Seropositive for the human immunodeficiency virus (HIV) - Pregnant (positive total HCG) or breastfeeding - Presence of large accumulation of ascites or pleural effusions, which would be a contraindication to the administration of methotrexate for GVHD prophylaxis - Known severe or life-threatening allergy or intolerance to ATG or cyclosporine/ tacrolimus - Planned administration of alemtuzumab (Campath-1H) or other investigational agents as alternative agent for GVHD prophylaxis - Concomitant enrollment in a Phase I study - Positive patient anti-donor lymphocyte crossmatch in HLA-A or B mismatched transplants; the definition of match is in Section 2.2.1; the crossmatch would only apply to mismatches at HLA-A or B, not DRB1 or HLA-C - Prior allogeneic marrow or stem cell transplantation - Patients with prior malignancies except resected basal cell carcinoma or treated carcinoma in-situ; cancer treated with curative intent less than 5 years previously will not be allowed unless approved by the Medical Monitor or Protocol Chair; cancer treated with curative intent more than 5 years previously will be allowed