It is an interesting topic. I think we will all have to be pretty careful if we want the thread to stay open as it is potentially going to get into contentious territory.
My background is a I was raised extremely religious, went through a period of agnosticism and a brief period of atheism in my very early 20s. But ultimately I returned to belief in God (for me it was a long process of reading philosophical arguments for and against, and having different experiences). Just my personal belief, not something I am interested in pushing on anyone else. I also found, despite moving towards agnosticism and atheism I still tended to do things like recite the Lords Prayer or the Rosary during things like heavy turbulence on a plane. Generally I am fairly skeptical of anything (not just supernatural claims but any, without evidence to support them), but I am always interested in other peoples experience and hearing what they believe about the world.
I have had a few experiences I can say felt supernatural to me. Whether they truly were or not, I can't say with any degree of certainty (I can definitely find plausible wordy explanations for them). At the same time, I am persuaded that two were at least genuine. The first experience was one I am quite convinced was a product of lack of sleep and medications I was given following a surgery. I saw the classic little green men dancing on my chest at night. Even as it was happening I was convinced it was a hallucination (though it came during a time where I did feel the walls between the afterlife were seeping into real life: after coming home from the hospital I had this dread that I had died and was in purgatory).
I've had two experiences though I feel were real and I would describe as religious experiences. And since those two events, I've continued to feel a presence at times. I don't think I can get into them without getting too deep into religious territory. For me, the experiences were profound and life altering.
Another experience isn't my own, but when my grandfather was dying he began talking to deceased relatives as though they were there. This was in maybe the last few weeks before he passed where it you could tell he was leaving. I honestly didn't know what to make of it. Part of me said it's just his mind being affected by the dying process and memories surfacing (he was also hallucinating bears at the time) but I also found the conversations very compelling and had a nagging 'maybe he really is talking the them' feeling.