I would guess that nearly every religious practice includes some notion of purification and that most, if not all, of those practiced by Christians were borrowed and adopted from pagan religious practices that predate them.
As to what a person would be purfied from (whether by bathing, by smoke and fire, or use of a scourge to focus their attention) it need not be tied into the Christian concept of sin - we give our homes a good cleaning every now and then to get rid of clutter and grime and most of us feel more centered, calm, and uplifted once it's done because it's a more pleasant environment. We strip off our work clothes after a day's work in part because it helps us transition away from the attitudes and needs of that role, and shower or bathe to relax, feel clean, strip away the layers of environmental clutter on our bodies and get back to ourselves.
Cleansing and purfication in a spiritual sense has the same purpose - to clear away the mental, physical and emotional debris left behind by daily living. Thoughts and attitudes that were useful and necessary but are no longer achieving their purpose are cleared away symbolically - the symbols of the act trigger our senses and help us remember to let go and get back to who we are at the core and to make way for whatever spiritual experience will follow.