I know I'm prone, but surely I can't be the only one that suffers this problem.
Problems with perceptible flicker are rare above 40-50 Hz, which is why motion pictures have been able to get away with 48 fps (24 images per second, each projected twice) for decades. Conventional television also gets away with 50 or 60 Hz, with two interlaced half images projected at half this frame rate.
I've never had any problems with 60 Hz and in fact I'm using it now. A small minority of people might still see flicker at that rate under some conditions. Bad conditions include high brightness images, seen in peripheral vision, in a dark room. The effect diminishes very rapidly at the high end with increases in refresh rate, so even a small increase might make the flicker "go away."
The type of display makes a difference. CRTs with their flying dots are much more prone to produce perceptible flicker than flat panels, since the latter are more or less continuously lit. The only problem with flat panels is possible slight smearing of motion with fast animation, but that problem is rapidly disappearing as flat panels advance.
What really used to irritate even me (and I'm not very sensitive to flicker) was low refresh rates on a CRT with interlace. Thank goodness that's history now. I was surprised by how many people weren't bothered by it at all, which shows how much individual variation there is. In fact, I'm surprised by the truly terrible images that people are willing to tolerate sometimes. I guess they don't care how much eyestrain they get.