For me these experiences came as part of the package of a psychotic break. At the end of 2005 when I had my second episode, shortly after it I started having what people call "out of body experiences" (OBE's). They usually happened spontaneously either while I was falling asleep or just about to wake up. I learned to control the state so that I would stay in it and experience it, while feeling at all times I was able to move myself to full consciousness and an awaken state if I wished to.
The best way I can describe this is that you have a somewhat dulled awareness and you have full memory of what transpires, unlike in an ordinary dream, you seem to have bodily sensations but not from your actual physical body. The environment you find yourself in and what you experience is still though of a dreamlike nature, so part of the brain that does the dreaming is still active. What one experiences is a kind of virtual reality which convinces you about its reality, much like we do in dreams with the difference that we know that what we experience is an "OBE". After several such experiences I have come to realise that these states are not of any mysterious nature nor do you "go elsewhere". I think one is immersed in his/her own subconscious but you interact with the content in a conscious way. Perhaps that is the value of all this, not the unprovable metaphysical theories people have put forward. You tap straight into the core of your being and you interact with it.
For about a year, between 2005 and 2007, I read and practiced several techniques such as meditation and more or less was set on a shamanic quest phase. I really see no metaphysical connection with all this, unless one simply chooses to believe the mythology behind them. What I do see though is that they bring you in touch with yourself, rather they can be useful in making you see below the artificial concreteness of concepts that we arbitrarily choose to build our lives around. In a way a shamanic quest brings one in touch with the true nature of a human being, which is more animal rather than of a logical abstract being.
What I have found out during those experiences is that what underlies the human psyche and mind is a mechanism that all humans and potentially other animals share. Apart from the ability to use our senses and store experiences as a learning mechanism for our survival, we have inner default systems that allow us to function (or not...!) in the face of uncertainty. These mechanisms are archetypes that function almost on their own and come to the surface under intense pressure or when we find ourselves lost in a situation. It is very close to what Carl Jung described as archetypes of the subconscious. These give rise to mythologies and religions, a kind of personification of bad and good, which are at the bottom the only two states we use to classify things we experience. "Bad" is anything that threatens our existence or hurts us (physically or emotionally), death being the ultimate "evil" which we try to avoid at all costs. "Good" is anything that soothes or pleases us, or secures our survival. On these two very basic and real functioning modes we have based then our abstract concepts, our religions and the gods that some of us choose to believe.
Even for an atheist, it is really hard work to keep these automatic responses at bay. They are so hardwired within us that they come to the surface almost on their own. Particularly in high stress situation, or in mental illness, they come to the surface as a means to explain what we experience which is so far out of our normal experience that we somehow have to use mythology to make sense of it. That is the other dimension also of modern man: we are trained from a young age to want to make sense out of everything, to find its causality so to feel safer with everyday situations.
I think that the way forward is not to seek through religions to find truths or meaning to what our reality is. They come from very distant times in the past, in some ways more correct but in many ways so out of date that they have no meaning in the face of our modern knowledge about Nature and ourselves. It is interesting to notice the similarities of all such religions, but not because they tap into some metaphysical source of truth but because they come from within human beings across the globe and time. They serve as proof that the underlying mechanisms of the human brain are universal among humans, they are the common denominator that can link us together if we correctly set our reference point in this reality.
It is the only reality level we can experience and I also believe the only one that exists for us. If we are so prone to make "good" choices that ensure our survival and minimise our suffering, then such a choice is collaboration and co-existence as it enhances mutually our survival.