I have not had one of these experiences, but I gather that they can be very convincing. I wonder if faith arises in part from some sort of flaw in the wiring of our brains.
I haven't had one either, but I was there shortly after my cousin had one. He explained it as a sense of euphoria and acceptance of everything, and he swears it wasn't caused by any drugs or anyhting external to his body. He said he could easily see how a person with a religious mind set could have felt it as the poresence of god, but being an atheist, he viewed it more as an example of the complexity of beauty of the human mind/body.
These sort of transcendental experiences are rare, but seem to be hardwired into our brains, either through some as yet unknown benefit, or through a misfiring or miscommunication in the brain, akin perhaps to deja vu. The rarity of the experiences, and the peace it gives, grant the experience something mystical, magical, or otherwise mysterious. As pattern seekers, we try to quantify and describe these passing experiences and forever seek after them again by whatever means we find the most likely.