The scientific evidence backing up the health benefits obtained by neurofeedback training is abundant and easily accessible online.
Biofeedback devices, including the use of neurofeedback, are regulated by the Food and Drug Administration and indicated for relaxation training.
A lot of the research has been done on attention deficit and a Norwegian study found neurofeedback training to be just effective as methylphenidate (common brands: Ritalin, Concerta, Daytrana, Methylin) for alleviating symptoms of children with ADHD.

Clinical trials related to neurofeedback are available on PubMed database: http://www.ncbi.nlm.nih.gov/pubmed/
Research specifically related to NeurOptimal® is available on Zengar Institute website: http://www.zengar.com/research

Momentum Wellness

A growing number of holistic health practitioners and psychotherapists are adding neurofeedback to their practice as reported in this article from the Washington Post:

http://www.washingtonpost.com/national/health-science/therapists-are-using-neurofeedback-to-treat-adhd-ptsd-and-other-conditions/2015/01/16/b38e6cee-5ec3-11e4-91f7-5d89b5e8c251_story.html



Coaching and Neurofeedback

Below are a few references illustrating the extent and state of the research on neurofeedback:


Bessel Van der Kolk: The Body Keeps the Score: Brain, Mind, and Body in the Healing of Trauma, 2015.

Hanno W. Kirk: Restoring the Brain: Neurofeedback as an Integrative Approach to Health, 2015. 
Maleki Leila: Depression and Neurofeedback, 2015.

Robert Hill & Eduardo Castro: Healing Young Brains, the Neurofeedback Solution, 2009.

Gyorgy Buzsaki: Rhythms of the Brain, 2006.
Hammond, D. C. (2005). Neurofeedback treatment for depression and anxiety. Journal of Adult Development, 12, 131-137.
Robbins, James: A symphony in the brain: The Evolution of the New Brain Wave Biofeedback. 2005.
Van der Kolk, B. A.(2005). Clinical Implications of Neuroscience Research for the Treatment of PTSD. Annals New York Academy of Sciences.

Monastra, V. J., Monastra, D. M., & George, S. (2002). The effects of stimulant therapy, EEG biofeedback, and parenting style on the primary symptoms of attention-deficit/hyperactivity disorder. Applied Psychophysiology and Biofeedback, 27, 231-249.
Davidson, R. J., Jackson, & D. C., Kalin, N. H.(2000). Emotion, plasticity, context, and regulation: Perspectives from affective neuroscience. Psychological Bulletin, 126(6), 890-909.

Research on Neurofeedback