you can check out enrolling stem cell trials for MS at www.clinicaltrials.gov;
just type in "multiple sclerosis" and "stem cell" into the search bar for instance
One of the more well know pundits is Dr. Richard Burt (Northwestern University, USA) who is involved in stem cell trials for various autoimmune diseases. He is quoted as saying "no inflammation, no response." In other words, he has mostly had success in individuals with signs of active inflammation (clinical relapses, new lesions, gadolinium enhancing lesions)
Here is an article on the subject: http://msj.sagepub.com/content/18/6/772.long
The general theory behind "stem cell therapy" in MS is to use cytotoxic agents which deplete the immune system. These agents are known to be effective in MS and are probably most of the reason for the short term benefits. The idea of using stem cells as rescue therapy rather than a simple autologous bone marrow transplant is to minimize the risk of reintroducing an immune system which is pathological. In other words, the idea is to kill your autoreactive immune system and to reintroduce a benign immune system...at least theoretically. The idea of using stem cells is somewhat sexy as one visualizes magical cells crawling into the brain and spinal cord and regenerating axons and myelin, but there is no evidence that this actually occurs. Again, the main symptomatic benefit is likely due to the cytotoxic agents.
Dr. Burt has used things like cyclophosphamide (known to be effective in highly active MS), alemtuzumab, and anti thymocyte globulin.
needless to say, these drugs have significant side effects.
For instance, cyclophosphamide (cytoxin) can cause hair loss, GI upset, hemorrhagic cystitis, immunosuppression leading to infection, anemia, and infertility. Autoimmune diseases have also been reported in these trials.
Generally, people advocate the use of such treatments for those with highly active relapsing multiple sclerosis unresponsive to standard therapies. This may be a smaller and smaller group of people with tysabri/campath/rituxan being readily used. Of course, you also have to be willing to risk the nasty or even potentially fatal side effects