Most tumors rely on a small population of cancer stem cells, which can be thought of as the "evil twins" of normal, "good" stem cells: rather than dividing to repair and heal tissue, they divide to form tumors. The cancerous cells can cloak themselves from the immune system and avoid attack, which is how they survive even after chemo and radiation. Clinical trials in California are testing a treatment to identify and "uncloak" the cancerous stem cells from the immune system, and to make sure they are completely wiped out by treatment, reducing the chance of a relapse.
In leukemia, there is a population of cells, known as leukemia stem cells, that are resistant to treatment that works on other leukemia cells. Scientists are investigating the use of drugs that can specifically identify and then kill these leukemia stem cells. In essence, this type of therapy might not be classified as a stem cell therapy, but rather a therapy that treats a disease caused by stem cells.
After a heart attack, many patients are left with scar tissue around the heart. Scientists are using heart stem cells to promote the self-repair of the heart. In some cases, these can be delivered by the blood instead of being injected directly into the heart. Clinical trials are underway now to test this approach.