Well, if there is a word that better describes what we term spirituality, I'll be happy to use it.
It probably is an overly used word, particularly to those who have alternative beliefs and are allergic to traditional organized religions, but words that describe non verbalized experiences or emotion run that risk...we spout on a lot about love a lot too, but it's probably a subjectively different experience for each person who claims the emotion.
In strict dictionary terms, religion and spirituality are actually synonyms...they are considered at least to some degree synonymous, but words change with usage, and more recently, people have begun to make distinctions in the way they use those two terms.
People are trying to find a way to express the internalized experience of transcendence, which is a real psychological phenomenon, it can be scientifically measured as positive changes in brain chemistry, brain activity and physiological response, as opposed to ritualized and instititutionalized expressions supposedly based on such experiences.
This is because, in part, there is a need to differentiate. The personal, subjective experience has always been there, but the ritualized expression of it, the community institutions are not always satisfying and for some people not only unnecessary, but actually detrimental to the experience of trancendence.
They serve two very different functions, for one thing. Ritual binds us socially, gives us commonality as it recognizes important personal or natural events, such as personal rites of passage or events in nature that effect us all. Transcendence is personal, entirely subjective and difficult if not impossible to share on a community level.
Priests or clergy in human society now mainly serve ritual and social functions, but do not always accomodate or facilitate personal transcendence, inner emotional or psychological exploration, although they can and some do specialize in counseling or psychological counseling. There were other recognized social roles in other societies that did recognize the power of such experiences, the shaman, the yogi, the medicine man, but it's hard to find a contemporary counterpart to that in modern religion, except, interestingly enough in modern psychology.
Today, it's the therapist, whether affiliated with a religious entity or not, who guides us on our personal inner journeys and helps us make sense of them. They even use some of the same tools, hypnosis or various relaxation techniques, even drugs, when called for, to assist that. I've heard many in that sort of work describe psychologists as the secular shamans or priests(in the older, more basic sense of spiritual facilitators, not as enactors of ritual) of our modern culture, and I believe that's true.
Which just goes to show you can do such things without the context of specific creed or religious doctrine...they just are part of human nature and always have been.