Psychedelic perceptions without drugs?

What are the ways that one can have the same (or nearly the same) experiences of psychedelic drugs WITHOUT using drugs or any external stimulant? I am looking for ways to have mystical, paranormal, spiritual, etc. experiences by committing to some discipline, such as focussed breathing or rosary repetition. I know of the Hindu/Buddhist systems so I need other systems of thought and discipline whose aim is to "experience" the divine using certain means of exercises, prayers, etc. Thanks.