I do at times, and people who know me well are no longer surprised by it. It does not happen frequently, but when it does it is beyond amazing and always a great bracha.
I will relate an experience and try to be very discreet about it (v’hamayvin yavin). I work in a field in which I come into contact with women on a regular basis. One time, a woman came into my workplace, and I directed her to the area that she needed to be, waiting for her to let me know when she needed me. Typically, I would not be called for about 1/2 an hour or longer. After 15 minutes, a disembodied voice in my head said, “Check on the woman in (the area where I had sent her).” Normally, I would never do that – it would be considered a no-no (kind of like interupting someone during Shmoneh Esrai). But I got up and went over to her to see if everything was ok, and literally the EXACT SECOND I approached her, her eyes rolled back and she fainted. Had I not been there to catch her and cushion her fall, she would unquestionably have struck her head on an extremely hard object in the area, based on the direction in which she fell. I do not want to think of what the consequences could have been. And the first thing I thought was Thank you, Hashem for putting me in the right place at the right time. This ended as a Hatzolah call, but B”H she was ok in the end.
As I said, it does not happen often, but I think each of us has the R”HK moment, and we don’t necessarily recognize it when it happens. We are all meant to have a level of nevuah of some type, as Am Yisroel, and I believe that sometimes Hashem allows us to have a taste of what that means, because something good is meant to come out of that moment.
What most people experience with “sixth sense” IMO, is more the great ability to discern body language and read inflection of tone. Haven’t you ever met someone who looked harmless, but instinctively you did not trust that person, then it turned out he was a Ponzi scheme goniff or the like? Some people are very adept at subconsciously noting hidden signals and vibes that are being given off. If we want to call that a sixth sense, it makes (sixth) sense. It really is more a case of excellent powers of observation.