Hematopoietic Stem Cell Transplantation for the Treatment of Patients With Fanconi Anemia Lacking a Genotypically Identical Donor, Using a Chemotherapy Only Cytoreduction With Busulfan, Cyclophosphamide and Fludarabine

Inclusion Criteria: * Patients must have a diagnosis of Fanconi anemia (confirmed by mitomycin C or diepoxybutane \[DEB\] chromosomal breakage testing at an approved laboratory). * Hematologic Diagnosis and Status - Patients must have one of the following hematologic diagnoses: * Severe Aplastic Anemia (SAA) with bone marrow cellularity of \<25%, or Severe Isolated Single lineage Cytopenia AND at least one of the following features: * Platelet count \<20 x 109/L or platelet transfusion dependence\* * ANC \<1000 x 109/L * Hgb \<8 gm/dl or red cell transfusion dependence\* * Myelodysplastic Syndrome (MDS) (Appendix 1: MDS Classification) - MDS at any stage, based on either one of the following classifications: * WHO Classification * Refractory anemia and transfusion dependence\* * Any of other stages * IPSS Classification * Low risk (score 0) and transfusion dependence\* * Any other risk groups Score \> or = to 0.5 * Acute Myelogenous Leukemia * Patients with acute leukemia are included in this trial in remission, refractory or relapsed disease. * Transfusion dependence will be defined as greater than ONE transfusion of platelets or red blood cells in the last year prior to evaluation on protocol. * Donors: * Donor choices will be determined by the investigators at each of the centers according to their own institutional criteria. * All patients evaluated at trial sites and eligible for this trial by virtue of disease and lack of an HLA-genotypically matched related donor will be captured in the database of this trial. Patients who will be enrolled on this protocol must have one of the following donor choices: * HLA-compatible Unrelated volunteer donors * Patients who do not have a related HLA-matched donor but have an unrelated donor who is either matched at all A, B, C and DRB1 (8/8) loci or who is mismatched at 1/8 loci (A, B, C or DRB1) (7/8) as tested by DNA analysis (high resolution), will be eligible for entry on this protocol. * HLA-mismatched Related donors * Patients who do not have a related or unrelated HLA-compatible donor must have a healthy family member who is at least HLA-haplotype identical to the recipient. First degree related donors must have a normal DEB test. * The donor must be healthy and willing and able to receive a 4-6 day course of G-CSF and undergo 1-3 daily leukaphereses. * Related and Unrelated donors must be medically evaluated and fulfill the criteria for collection of PBSCs as per institutional guidelines. * Patients: * Patients and donors may be of either gender or any ethnic background. * Patients must have a Karnofsky adult, or Lansky pediatric performance scale status \> or = 70%. * At the time of referral for transplantation, patients must have no co-existing medical problems that would significantly increase the risk of the transplant procedure. * Patients must have adequate physical function measured by : * Cardiac: asymptomatic or if symptomatic then 1) LVEF at rest must be \> or = to 50% and must improve with exercise or 2) Shortening Fraction \> or = to 29% * Hepatic: \< 5 x ULN SGOT and \< 2.0 mg/dl total serum bilirubin. * Renal: serum creatinine \< or = to 1.5 mg/dl or if serum creatinine is outside the normal range, then CrCl \> 60-ml/min/1.73 m2 * Pulmonary: asymptomatic or if symptomatic, DLCO \> 50% of predicted (corrected for hemoglobin) * Each patient must be willing to participate as a research subject and must sign an informed consent form. Parent or legal guardians of patients who are minors will sign the informed consent form. Assents will be obtained as age appropriate. * Female patients and donors must not be pregnant or breastfeeding at the time of signing consent. Women must be willing to undergo a pregnancy test prior to transplant and avoid becoming pregnant while on study. Exclusion Criteria: * Active CNS leukemic involvement * Female patients who are pregnant (positive serum or urine HCG) or breast-feeding. Women of childbearing age must avoid becoming pregnant while on study. * Active uncontrolled viral, bacterial or fungal infection * Patient seropositive for HIV-I/II; HTLV -I/II