When should bone marrow transplantation be performed?

When in remission. The other part of the answer is the timing of the transplant for the above disorders. While it is common to consider transplant as a 'last resort' or 'only if the disease relapses', that usually is the wrong time to do it. Transplants of all types work best if the patient is robust and in remission at the start. That's often why it is so hard to determine the 'right' time to take the risk.
Leukemia/Marrow Dis. The actual indication depends on if it's a child or an adult. Common reasons are red blood disorders (aplastic anemia where red cells aren't made) and cancers of white blood cells (leukemia or lymphoma), multiple myeloma, very aggressive cancer treatments, inherited (genetic) diseases (such as thalassemia), and immune-system disorders (such as congenital neutropenia/low white cell count.

Related Questions

When was the first bone marrow transplant performed?

Which type? The first bone marrow transplant in humans was between identical twins in 1958. Autologous transplants (a patient to him or herself) soon followed. In 1968, allogeneic transplants based on HLA tissue typing were performed.