Spinal cord injuries are indeed one of the types of injury for which stem cells hold potential for treatment.
Thanks to the findings from a large number of animal studies scientists are working on the following ways that stem cells may contribute to repair the spinal cord:

• they may be used to replace the nerve cells that have died as a result of the injury;
• they may be used to generate new supporting cells that will re-form the insulating nerve sheath (myelin) and, consequently, stimulate re-growth of damaged nerves;
• when introduced into the spinal cord shortly after injury, these cells may protect the cells at the injury site from further damage, by releasing protective factors.

Scientists in the United States are hoping to start a clinical trial to investigate the safety and benefits of using a type of nerve cell (called oligodendrocytes) made from human embryonic stem cellsⁱ in treating recent spinal cord injuries. They have obtained promising results with these cells in rat models of spinal cord injury, and, if granted a licence by the American Food and Drug Administration, hope to test this therapy in a limited number of patients.

Other studies have shown that cells in the lining of the nasal cavity help regenerate spinal injuries when transplanted into the spinal cords of injured rats. Researchers are planning to transfer this approach to patients with a specific type of spinal cord injury, called brachial plexus avulsion, within two to three years' time. In this type of injury, which occurs most commonly in motorcycle accidents, the nerves of the arm are separated from the spinal cord, resulting in paralysis of the arm.

Relevant links:
Professor Geoffrey Raisman's research page - using cells in the lining of the nasal cavity for spinal cord regeneration
The National Institute of Neurological Disorders and Stroke
European Spinal Cord Injury Federation