I've been (un)lucky enough to have seen half a dozen while hunting. Most have not seen me, but I have encountered them at very close range on two separate occasions. One was while hunting in Eastern Oregon. I decided to stalk up the side of a hill with tall grass and wind blowing right at me. It was a good idea, seeing how a cat had decided so as well. When it's head popped up above the grass and looked at me, I froze and stared right back for at least an hour (maybe 10 seconds in real time), before it bounded off in the other direction. When I resumed my stalk, I ran right into a cow elk that I managed to shoot a foot or so over her back. Maybe it was the nerves.
On another occasion here in California, I came across some fresh deer tracks with even fresher lion tracks on top of them. I followed the tracks for a bit and then heard a hiss from a bush about ten feet behind me. I turned in time to see the biggest cat I had ever encountered bounding away from me. Had he decided to pounce, I am certain I would have been done for.
We get a lot of reports in California recently regarding cat attacks on dogs and occasionally on children or sitting adults. We are no longer allowed to hunt them here and they are starting to become a bit more daring. I imagine there will be more attacks in the near future as climate change increases drought weather here and the complete lack of any predators increases their numbers.