I read a book on the anthropology of religion and it introduced a concept that was at once obvious, but seemed to fly past the heads of every atheist or religious person I've heard discussing it.
Totems are things which stand for other things, in a symbolic sense. The important thing about totems is that they involve no supernatural claims, but can still be the basis of spiritual rituals. The point of totems is to draw a poetic allusion between two concepts. Instead of being argued for the connection is engrained through ritual acts.
The example the text gave was communion, Christians don't actually believe they are eating a dead guy when they partake of bread and wine, it's an act which stands for something else. Just as what is eaten will be digested and then constitute the body, the teachings of Christ will be digested and constitute the body of the follower (ergo, salvation).
This act draws upon Jesus Christ: the totem, not as the supernatural son of God or a historical figure, simply as a symbol. What I noticed more and more as I reflected on religious ritual was how crucial the totem was in each case. Rituals are powerful, symbolic acts and totems are the symbols the practitioner is trying to understand. Rather than a mental act like contemplation, however, rituals rely on physical acts to create understanding.
Mythology is always the context in which these rituals take place, but they are not the immediate foundation. Consequently, there is nothing to be believed or doubted in a pure ritual, an atheist can do it as well as anyone, all that is required is the intention to have the relevant insight unveiled.
This to me is the essence of spirituality: a physical act used to create a mental state, or a mental act used to create a physical state, each reinforcing the connection between mind and body. For a culture which often views mind and body as inevitably divorced, this is tremendously useful.