It depends on what kind of stem cells you're talking about.
The first type to become widely available will be autologous hematopoietic stem cells. The most advanced trial is a phase 3 (http://www.clinicaltrials.gov/ct2/show/NCT00273364
), but it hasn't completed enrollment yet and is a 5 year study, so it would be at least 6 years until approval. There are some with MS who have already been treated with this type of stem cells without participating in a trial, I think. They initially only did this type of transplant after wiping out the immune system entirely, but are now investigating how well these cells work without a complete "rebooting".
Next up will be mesenchymal stem cells. There is a small phase 2 trial in Israel that might be complete now (http://www.clinicaltrials.gov/ct2/show/NCT00781872
). There was a small trial in Iran that is complete. There is a trial ongoing in the UK (http://www.clinicaltrials.gov/ct/show/NCT00395200
) and there is a US trial starting soon, I think at the Cleveland Clinic. I would guess this type of stem cell treatment would still also be at least 6 years off, if not more.
For other types (e.g. neural precursors or oligodendrocyte precursors), they are just starting phase 1 trials now, so that puts them at least 8 years out, if not longer.
Hope that helps, sorry I couldn't come up with an earlier date.