I've had plenty of things happen to me that I couldn't explain, but I wouldn't consider them supernatural.
For example, part of my job involves confined-space entry (CSE): I have to go into manholes and pipes every now and then, to inspect them for damage, verify the construction, run tests, collect samples, and all that. It's all part of the glamorous job of being a water engineer. Sometimes, I get a premonition or a 'gut feeling' that something isn't right, and I'll call off the entry...and then discover that the atmosphere in the pipe was harmful and the 4GD was out of calibration, or my retrieval harness was damaged, or whatever.
Now I'd love to attribute that 'gut feeling' to my dad, rest in peace, looking over me and keeping me safe. It's also possible that it is my own guardian angel, or an alien that has an interest in my lifespan, or nanobots that the government injected me with, or a safety charm that my grandmother placed on me when I was born (she was very superstitious). But it's most likely that it is the result of the hours of rigorous training, my years of CSE experience, and the lengthy and repetitive annual certifications that have all sharpened my awareness. I've been trained to be vigilant (paranoid?) to danger, to follow regulations to a T, and to react quickly in danger, and that is the most likely source of my premonitions.
Note that I said "most likely." Occam's Razor says that the easiest answer is also the most likely, but it's not evidence. Since there's no safe way to test that theory (sending untrained people into confined spaces as control, for example), and since we don't have the technology to detect, measure, and predict the impact of ghosts/angels/aliens/nanobots/charms, my premonitions remain unexplained.
Unexplained, but probably not supernatural.