Wow so many agnostics
People can have a sense of the divine ground expressed in various ways, but a few do experience the literal "super natural" event. I think though that your life generally needs to be quiet enough to 1. Be receptive to it, and then 2. To then actually receive it. Thats why monks tend to have spiritual experiences, the isolation makes them quite receptive to them.
When I was 22 I had a "visitation" by a group. It was around 3am and I was fast asleep. My bed was right against the window with the blind drawn down so no possible light could get in. Something tapped me on the shoulder and woke me up. I rolled over in bed not thinking it was anything malevolent to see what was what. There beside me I was being visited by a group. There was one tall form in front of about half a dozen others.
I couldnt make out details about them, they were more like energies, the afterglow of a bright light, but I do remember how tall there were! There was also this projection of light from the window onto this group like some door was opened, but the blind was drawn.
At first I thought I was dreaming, so I did the old movie trick got up on my elbows staring at them and then blinking hard a few times. They didn't go away.
I always swore that if I saw something like that that I'd reach out and touch it, you know like Dan Ackroyd in Ghost Busters "Get her!" but NO WAY.
I got shit scared then and just wanted them to go away. My defense mechanism was to turn around towards the blind, pull it back and look outside to see where the fuck this light was really coming from (really I just wanted them to go away). I looked outside and it was pitch black out there. I turned back and they were gone.
I tried to go back to sleep but couldn't and got up really excited and turned the light on. My life changed dramatically a few months after that in so many ways, moved out of home, got my first job and my first boyfriend. All of this was very significant because I hadn't ever been independent, gay or employed, ever! Looking back I think the experience gave me "hope" at a time when I was very isolated.
Haven't had an experience since but I do get quite sensitive to this "otherness" when significant things are about to happen, like falling in love or a relative is about to die. It's too profound to comprehend though, its like there are major murmurings of purpose and "otherness" going on all the time.
My mother is a lot freakier / freakable and sensitive to it than me. I swore I heard her voice calling my name once in my head when something bad was happening. It was also fun telling her about the above just to freak her out
Strangely I don't feel that experience has made me more of a believer. I feel a sense of the divine ground regardless. I'd like to think everyone does in their own way.
By the way, I am not religious at all.