Some say they were travelling down a dark tunnel towards a bright, warm light. Others say they saw their body in the hospital bed from above or experienced a mystical oneness with the universe.
Are these "near death experiences" real or just the product of disorganised activity in the dying brain? The psychologist Susan Blackmore thinks she can find out.
Dr Blackmore says that we could find out what is going on inside the brains of dying patients by scanning their brains with fMRI or PET.
What happens when we die? Surely everyone wonders about this very human question, and it's certainly caused much dissent between religion and science. While most scientists think that death must be the end of personal consciousness, most religious believers expect their soul or spirit to survive.
Brain scanning would allow scientists to answer some basic questions for the first time, she says.
...we would be able to test theories about how near death experiences and mystical experiences are generated in the dying brain, and answer questions about the timing of the experiences. Perhaps even this would not resolve the final question once and for all, but it would certainly bring us a lot closer to knowing what happens when we die.
The idea is her contribution to a series of blogs about the most important psychology experiments never carried out. The British Psychological Society have asked top researchers for their suggestions and the results will appear on its Research Digest blog this week.
Other suggestions include Vaughan Bell's of the Insitute of Psychiatry who proposes employing private investigators to follow people who are convinced they are being persecuted to check whether they really are - that in itself might freak them out a bit.
Martin Seligman of the University of Pennsylvania wants to try changing the way psychotherapy is done. Rather than sitting on the couch and talking about your problems maybe focussing on what is going well in your life would be more effective.
What do you think is the most important psychology experiment - for that matter any experiment - ever done?
Dr Blackmore appeared on the Guardian's Science Weekly podcast in April.
