I am a very practical, non-religious person but there have been two occasions in my life when I have felt 'something'. One was on a visit to The Grand Palace in Bangkok. We went into the meditation room and a feeling of peace immediately came over me and I could have just stayed there.
Another time was in a yoga lesson. We had a very good teacher and after the yoga there was a meditation time. As I sat on the floor leaning on the wall, I felt myself rise above my body and I was looking down on myself for a few seconds. It wasn't frightening but I remember it vividly.