Spirituality
Spirituality, in a narrow sense, concerns itself with matters of the spirit. Spiritual matters are those involving humankind's ultimate nature, not only as material biological organisms, but as beings with a unique relationship to that which is beyond both time and the material world.
—http://en.wikipedia.org/wiki/Spirituality
Spirituality is not just a general term that describes humanities attempt to relate to transcendant ideas, but also individuals who do not define themselves within any religious camp, but nevertheless have religious practices and subscribe to specific religious ideas. They often refer to themselves as being spiritual, rather than religious.
I could hardly deny the existence of individuals who very sincerely and devoutly take themselves to be the lone communicants of what we might call private religions. Typically these people have had considerable experience with one or more world religions and have chosen not to be joiners. Not wanting to ignore them, but needing to distinguish them from the much, much more typical religious people who identify themselves with a particular creed or church that has many other members, I shall call them spiritual people, but not religious.
-Daniel Dennett, Breaking the Spell