OK. I mean both, and can give different kinds of examples.
In Patanjali's yoga sutras, we're told that we can obtain definite knowledge on subjects through contemplation. This contrasts to the modern method of reasoning about sensate experience, performing experiments, and checking results. As I see it, that belief amounts to a kind of appeal to authority, an 'inner' authority, corroborated by the authority historically accepted religious teachers. So its a self-reinforcing belief system, and when they're wrong about stuff they're not very good about recognizing it and correcting it. So I'd write it all off as bullshit. Trouble is, I thought about this stuff with an open mind for about five years before I recognized it was largely bullshit, and it changed me somehow. Section III of the sutras describe mystic powers that a person can supposedly obtain through mental control. I have some of that now, not enough that I can prove it in a rigorous, publishable scientific sense, but enough to produce sufficiently objective results to know that I'm not delusional or seeing patterns where there aren't any. One aspect of this involves some kind of extra-sensory information about things that will happen, and its not information that can be extrapolated from past experience. One example I sometimes give is I dreamed of the airplane bird-strike and landing on the Hudson river during a nap a few hours before it happened, and I e-mailed the dream to someone before the event occurred. For the past several years this kind of thing happens to me almost daily, but usually not in relation to public events. And often the subjective or metaphorical aspect is strong enough that it doesn't sound very convincing to a skeptic. For example, on the morning of the school massacre last week, I woke up with the words "I hunt, therefore I am" in my head, from the song "Of Wolf and Man" from ~1990. At that moment I felt that I'm unhappy in life because I'm not true to my nature, which is to kill. Later in the day I recoiled from the predatory feeling after finding out what happened in Connecticut. That experience, having felt that aggression first, then its consequence, changed me a little bit in a way that I would not have changed otherwise. This subjective aspect of the experience is more valuable to me than something more objective like predicting a train wreck, because I can do something with it that makes a small difference. You can look at yourself and believe that you should be better than you are, but that only goes so far. When you feel and understand what something is in the same part of yourself that is that way, then you can move something.
I know that many other people have these kinds of experiences also. But usually they're prone to partially fabricating their experiences, or drawing unsupportable conclusions from them, and so are viewed as untrustworthy. Or they're more scientific and objective and keep their mouths shut because they don't want to be considered crazy. And a lot of people just ignore stuff that they don't know how to process, and don't explore such subjects enough to open the door very much to start with.
Second example: Gospel of Thomas, which the next poster quoted from. It contains a lot of cryptic stuff about reconciling and integrating the masculine and feminine parts of one's psyche. And it states that very radical results follow. The 'experts' mostly interpret this as advocating some kind of asceticism, and maybe that's even what it meant to the people who wrote it. But that's not what it means to me at all. I guess this is similar to the jnana yoga example. I think that the vision of escaping nature, which is central to Buddhism and similar Vedic doctrines, is wrong, and that the standard doctrine of karma is largely wrong. But if you do this thing of developing the capacity to feel, and relating that capacity to your will and other aspects of your mind, and not shrinking away from the difficult things you find out about yourself, it does do something significant.
Many early Greek Christians clearly believed that individual people could be perfected, and that this would result in an actual physical resurrection from the human condition. It seems doubtful to me that they were right: we all share a genome, and a psychological substrate, and even a physics, for the most part. To a significant extent we're locked into what we are and can't individually overcome it, at least not within the scope of a human life, by grace or otherwise. Usually this problem is addressed by watering down the doctrine so that it doesn't mean as much. For example, Paul said a man born of God can not sin. And yet, its generally acknowledged that all Christians sin. So it follows that Christians aren't really born again, have not really fulfilled the requirements for what was promised. What then of redemption? It will all be taken care of after we're dead. How convenient.
I realize that Christian faith is transformative for a lot of people, and I don't dismiss the value of that. My point is that its not transformative enough to be squared with the everlasting life vs eternal damnation difference in outcomes that the religion is based on. If you've been changed enough to justify eternal life in place of oblivion, then the differences in life should be comparably radical. If we have souls we have them when we're alive too, the condition of those souls does have outward effects. ("There is nothing hidden which will not become manifest.") For me one value of the older religious texts is the ideas haven't been watered down as much to reconcile them with the more depressing aspects of human life and natural history. Of course we do have to reconcile mystic ideas with reality if we're going to do anything useful with them, but its a project that requires a lot more work in that direction.
I have two problems with pretty much all "experts". One is that they're concerned with maintaining their position as experts, and generally won't engage with other people except insofar as it supports that. My other problem, which is closely related, is that they all regard some kind of philosophy or doctrine as authoritative, whether it is atheist science, or Jungian psychology, or Tibetan Buddhism, or whatever. And every one of these doctrines is both dated and intentionally skewed to give relative advantage to the priests and followers of it. It seems that nobody is willing and able to step outside of that and look honestly at everything. And so there are two factions, one that regards mystic phenomena as delusional, and one that embraces some preferred but largely unworkable explanation for such phenomena.
Third example: The I Ching. It works pretty well, both as a philosophy and as an oracle, even though the theory of five elements that its based upon is in my mind quite implausible. Jung was an 'expert' who understood that the I Ching works, and he described its working in terms of 'synchronicity'. Elsewhere he stated that the 'collective unconscious' is collective purely as a result of people being similar to each other, that there isn't actually anything magical going on. And so synchronicity all comes down to a combination of mechanistic effects and selective extraction of patterns from noise. That view allowed him to maintain his respectable reputation. But by leaving that unstated most of the time, and never confronting the contradiction, he also positioned himself as an authority on mystic phenomena that can't possibly be accounted for that way.
Other examples: Secret of Golden Flower, the Buddhist/Taoist text: to me its a form of mental yoga with a slightly different vocabulary. The Tao Te Ching: that thought does things also. Jumping back to what I said about becoming more psychologically developed....If you ask the 'who am I' question, in whatever manner, one effect it has is you learn to move your sense of identity. To some extent you may move it in a delusional way, but that's not all that's going on. For instance, you can give yourself out of body experiences even though superficially there isn't actually anything going "out of body", you're just manipulating a mental map of where you are. And yet, somehow you're doing more "just" manipulating a model, you can produce effects that can't be accounted for that way, such as moving objects without touching them. Your sensate reality is a model that connects to the world some way that is not currently explained, its more than just a physiological focusing and interpretation of electromagnetic and chemical information. When you find you can change it, and that you have some power to change who you are, this has results. The descriptions and explanations of this sort of thing in old scriptures may be wrong, but they're at least attempting to deal with aspects of it that aren't touched by modern scientific, philosophical, and scientific theories.
I think the philosophical aspects of all this are a lot more important than the pheomenological aspects. But its all interrelated, you can't be wrong in one area without being at least a little bit wrong in the other area also. You can't do real philososophy without a realistic view of how the world works, any more than you can do psychology well without any knowledge of neurology. So I think that modern philosophical views are severely distorted by the disconnect between mystic experience and scientific knowledge. Speaking for myself anyway. Even small steps in reconciling the two seem to produce fairly big experiential changes.
I guess I've got to stop somewhere, so I'll leave it at that.