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The God helmet is an apparatus developed by Stanley Koren and neuroscientist Michael Persinger that is placed on the head of an experimental subject to study the effects of subtle stimulation of the brain's temporal lobes by low frequency magnetic fields.
According to Persinger's accounts of his experiments, many subjects reported "mystical experiences and altered states" as well as a "sensed presence" while wearing the helmet. This detail was picked up in popular media and promoted in several TV documentaries, earning the device the nickname, "The God Helmet".
The basic foundations of Persinger and Koren's experiments have been criticized in the scientific press. The fluctuating magnetic fields generated by the helmet are approximately as strong as those generated by a land line telephone handset or an ordinary hair dryer, but far weaker than that of an ordinary refrigerator magnet, and approximately a million times weaker than transcranial magnetic stimulation. In short, the magnetic fields generated by the God helmet are far too weak to penetrate the cranium and influence neurons within. 
One study has claimed to replicate one of Persinger's early studies, They reported that their experiment ruled out suggestibility as an explanation for God Helmet results, and that an analysis of their subjects’ verbal reports revealed significant differences between the speech of subjects and controls, and less robust effects for suggestion and expectation. However, the study is published in the pseudojournal Journal of Consciousness Exploration & Research.
A prior attempt at replication published in the scientific literature reported a failure to reproduce Persinger's effects and the authors proposed that the suggestibility of participants, improper blinding of participants or idiosyncratic methodology could explain Persinger's results. The theoretical basis for the God helmet, especially the connection between temporal lobe function and mystic experiences, has been questioned.
Richard Dawkins had the device tested on him; appearing in the BBC science documentary series Horizon. He did not have a 'sensed presence' experience, but instead felt at times 'slightly dizzy', 'quite strange' and had sensations in his limbs and changes in his breathing. Persinger explained Dawkins' limited results in terms of his low score on a psychological scale measuring temporal lobe sensitivity.
Persinger and colleagues also developed a device nicknamed "The Octopus" which uses solenoids around the whole brain, in a circle just above subject's ears. Persinger’s research associate Todd Murphy, reports that his similar devices are able to modulate emotional states in addition to enhancing meditation and generating altered states. An experiment found no change in emotional responses to evocative pictures but said further investigation was required. 
- MichaelShermer.com - Out of body experiment (5:00 in the video)
- Ruttan, L. A., Persinger, M. A. & Koren, S. (1990). "Enhancement of Temporal Lobe-Related Experiences During Brief Exposures to MilliGauss Intensity Extremely Low Frequency Magnetic Fields". Journal of Bioelectricity 9 (1): 33–54.
- The Electromagnetic Induction of Mystical and Altered States Within the Laboratory. Journal of Consciousness Exploration & Research
- Science Channel clip of God Helmet
- Craig Aaen-Stockdale (2012). "Neuroscience for the Soul". The Psychologist 25 (7): 520–523.
- Tinoca,, Carlos A;; Ortiz,, João PL; (2014). "Magnetic Stimulation of the Temporal Cortex: A Partial “God Helmet” Replication Study". Journal of Consciousness Exploration & Research 5 (3): 234—257. Lay summary.
- Richards, P M; Persinger, M A; Koren, S A (1993). "Modification of activation and evaluation properties of narratives by weak complex magnetic field patterns that simulate limbic burst firing.". The International journal of neuroscience 71 (1-4): 71—85. Lay summary – " subjects exposed to a computer-generated wave form, designed to simulate neuronal burst firing, generated narratives dominated by more pleasantness and less activation than a reference group.".
- Granqvist, P; Fredrikson, M; Unge, P; Hagenfeldt, A; Valind, S; Larhammar, D; Larsson, M (2005). "Sensed presence and mystical experiences are predicted by suggestibility, not by the application of transcranial weak complex magnetic fields". Neuroscience Letters 379 (1): 1–6
- From BBC Two: God on the Brain
- Gendle, MH & McGrath, MG (2012). "Can the 8-coil shakti alter subjective emotional experience? A randomized, placebo-controlled study.". Perceptual and Motor Skills 114 (1): 217–235.
- Can We Be Good Without God?: Biology, Behavior, and the Need to Believe by Robert Buckman; page 92