In a conversation recorded among Richard Dawkins, Sam Harris, Daniel Dennett and Christopher Hitchens (you can find it on Dawkin's web site), a useful distinction came up: spiritual vs numinous. Numinous has to do with feelings such as wonder that occur to people. Such feelings are real experiences, but any connection to anything spiritual (non-material, gods, ghosts etc) has to justified separately.
Thanks for bringing this point up, Woodsy. I was trying to think of a good way to suggest that distinction. I had forgotten the idea of "numinous". I would posit that a sense of wonder - a sense of the numinous? - is a common trait shared across our species (although what constitutes "wonderous" would be different for different people, cultures, and times). I certainly feel a sense of wonder at many things in the world around me, but I've always been really uncomfortable with defining that as "spiritual" because of the association with gods, ghosts and things that go "bump" in the night.. "Numinous" sounds right.