Wikipedia does a great job of summarizing neurofeedback:   en.wikipedia.org/wiki/Neurofeedback

Really excellent site that organizes some of the most recent research in neurofeedback by diagnosis or problem:  www.eeginfo.com/research/

Site that compiles the latest research in neurofeedback: www.eegspectrum.com/Applications/InfoNetwork/

Excellent summary reviewing the effectiveness of Neurofeedback for ADHD:

Efficacy of Neurofeedback treatment in ADHD: The effects on Inattention, Impulsivity and Hyperactivity.  A meta-analysis. In EEG and Clinical Neuroscience (2009). 40(3), 180-189. Martijn Arns, Sabine de Ridder, Ute Strehl, Marinus Breteler & Ton Coenen

Summary or Full article

Article summarizing effectiveness for mood problems such as anxiety and depression:

 "Neurofeedback with anxiety and affective disorders" published in Child and Adolescent Psychiatric Clinics of North America - Volume 14, Issue 1 (January 2005)

A robust body of neurophysiologic research is reviewed on functional brain abnormalities associated with depression, anxiety, and obsessive-compulsive disorder. A review of more recent research finds that pharmacologic treatment may not be as effective as previously believed. A more recent neuroscience technology, electroencephalographic (EEG) biofeedback (neurofeedback), seems to hold promise as a methodology for retraining abnormal brain wave patterns. It has been associated with minimal side effects and is less invasive than other methods for addressing biologic brain disorders. Literature is reviewed on the use of neurofeedback with anxiety disorders...