This phase II trial studies how well giving a donor bone marrow transplant (BMT) works in treating patients with refractory Crohn's Disease. We will select patients with severe Crohn's Disease and active inflammation despite the best medical and surgical treatments. These patients must be healthy enough to undergo a transplantation procedure. They cannot have an active infection, and their heart, lungs, kidneys, and liver cannot be failing. The transplant procedure starts with chemotherapy and a small dose of radiation, to weaken a patient's immune system so that it will accept bone marrow cells from another person. After that other person's bone marrow cells are given to the patient, immune suppressive medicines are given to prevent the new cells from being rejected and to stop those cells from damaging the patient. After the new donor cells start to work, blood counts will rise and the new immune system will start to grow. During this time, there is a risk of infection. Antibiotics and anti-viral drugs will be given to prevent infection. When the new donor cells are well-established, immune suppressive medicines are discontinued. We will examine parts of the intestine that were inflamed before the start of the transplant procedure, to be sure the Crohn's Disease has disappeared after the transplant. Patients will be formally evaluated for Crohn's activity at around 100 days after transplant, and yearly after that for 5 years.