I had an experience like Bills, stone cold sober, no drugs. Laying on my bed 2 days after yet another episode involving yet another car crash and loss of job. Cry out to God, start praying and wham, this feeling of ectasy, love and being in the presence of something indescribably powerful came over me, then a feeling of calm and 'everything is going to be ok' and it was.
The only thing I can think to describe it would be like a hug from a parent when you're small and upset and then that makes everything better, but like 100 times that feeling and like I have since read from others who have had the same experience, a realisation that I had just been in the presence of God.