We live in a strange reality.
We see millions of colours where there are only variations in light frequencies. We hear sounds such as tree leaves rustling and ocean waves crashing, yet there are only sound waves. We feel temperature, pressure, weight, texture, balance, motion, while in reality there are only particles / waves with varying characteristics, constantly interacting with each other according to physical laws. What we experience as colour, sound, temperature, pressure, balance, motion, smell, taste, hunger, thirst, pleasure, pain, and the entire spectrum of emotions, are all in fact creations of the mind in an attempt to interpret the reality that it finds itself in. Physiologically this equates to a cocktail of chemicals and neural impulses, constantly swirling and surging around in the brain and nervous system. This definitely doesn't mean that what we experience is a false reality, but rather that it is an interpretation of reality; one that is both useful and necessary for survival and prosperity. After all, the man who could directly perceive quantum interactions won't be paying attention to the road. However, what I've just described falls very much into the category of 'normal' experience.
Despite the great strides that have been made through scientific observation and experimentation, people still experience the world in a mystical manner. And while the hypocrisy of most religions and their followers tends to make me shudder, there is an undeniable body of work from spiritual traditions world-wide that describe practices that can lead to a large variety of 'mystical' experiences. While I haven't personally had all these experiences as they're described, I've certainly had more than a taste. My curiosity in mysticism began with the experience of lucid dreams, which is consciously dreaming while asleep, and later astral projection, which is consciously dreaming while awake, although distinct from simple daydreaming in that there is the perception of a 'dream body' being inhabited and a 'dream environment' being explored. This, of course, leads to out-of-body experiences, in which the life force itself is said to escape the body. Anybody who has had enough of these will tell you that what is experienced while out of body is often more vivid, more intense, more 'real' than the real world, and I can corroborate this from my own experiences. Colours seem more brilliant, sounds are sharper, feelings are more intense, etc. Now, whether or not there actually is an energetic body that can leave the physical body is not the point I'm getting at. Of course it could just be that one enters a sufficiently altered state of consciousness where imagined experiences are perceived this way. The point I'm getting at, is that these experiences can be had with only a few months of diligent practice, and no religous symbols, incantations, rituals or gods of any kind are required.
Take up Buddhist meditation and you can eventually get to a point where perception of reality is drastically altered. With enough practice in vipassana, sensations are perceived as completely impermanent, in the sense that they appear out of nothing and then disappear again into nothing. This oddly agrees with the behaviour of particles at the quantum level, although serious Buddhists tend to urge people to not make that comparison. Eventually, the meditator will have an experience called enlightenment, in which all perception of sensations temporarily cease (as if the universe vanishes and then reappears again), and awareness of awareness emerges. What the benefits of meditating diligently for a few decades to have this experience are, are typically not disclosed by Buddhists that have accomplished enlightenment. (They tend to just smile and then say something like "you should go see for yourself.") Once again, I'm not making any religous claims about reality. My point again is that this experience can be had without any religous culture or paraphernalia. No gods or rituals are needed to sit on your butt and pay attention to what you are sensing. (Butthism, hah)
Other mystical experiences can lead to what is described as ecstasy and bliss, and they invariably involve altered states of consciousness (note that no drugs are required to induce them.) A new and rather fascinating spiritual tradition, called chaos magick, uses a practice called belief shifting in order to change their perception of reality routinely. They will take a dice and decide something along the lines of 1 = christianity, 2 = buddhism, 3 = atheism, 4 = hermeticism, 5 = shamanism, 6 = paganism, and then they throw the dice and take up whatever belief system is indicated for a month, and then change it the next month. They continually do this until the arbitrary nature of belief and perspective is understood experientially. Unfortunately, doing this can have some serious psychological effects on the self, such as ego deconstruction and close shaves with madness. However, whether they are invoking ancient egyptian gods or practicing magick like a thelemite, they inevitably experience way-out-there states of consciousness, although they will use the culture and practices of a religion or spiritual tradition to have those experiences.
Mysticism seems to be deeply ingrained into our minds, even if that part of the mind is ignored (commonly by both christians and atheists alike). Mystical traditions are also becoming more sophisticated and effective by laying out specific practices to take up in order to have certain experiences. (See Alan Chapman's "Advanced Magick for Beginners" for a step-by-step and alternate way to experience enlightenment. Just know that it's not for the light-hearted.)
Mysticism is always going to be around, even if it's only practiced by a small minority.
(Note: I won't be around at all times to respond to comments, but I will respond eventually when I can)