Yes, quite a few but only since I converted from Christianity.
Some experiences are ones that are a matter of interpretation: omens, but where the odds against their having been chance events are very high.
Other experiences, like direct contact with a god or the immediate granting of a prayer, do not allow for an alternative explanation. Well, I dare say out atheists will offer one, just as evolution deniers can come up with "explanations" of the evidence!
I don't think "inducing" applies: I do or say something, a god replies.
They seem to be quite common, although many people would describe as "religious" what I'd classify as emotional. A US survey showed around half of those questioned had had a religious experience, while a UK survey showed about two thirds. In the US, the respondents were given psychological tests and the proportion registering as suggestible was no more than average. In the UK, their eductional level was ascertained, and religious experiences were more common among those with higher education.
As the neurologists Eugene Aquili and Andrew Newberg observed, maintaining that people's religious experiences are caused by brain events is "equivalent to maintaining that their experience of the sun, the earth, and the air they breathe is reducable to neurochemical flux."