"Off the top of my head though, I cannot think of any lens with a minimum aperture between f/5.6 and f/8. It would have to be a non-constant aperture zoom, perhaps with a tele? It would be very tricky to be shooting and know that your minimum aperture just went from below f/5.6 to just above it!"
The Sigma Bigma and the Sigma 150-500mm are f/4.5-6.3 and f/5-6.3 respectively. They're the only ones above f/5.6 that I can think of, off the top of my head.
We get above f/5.6 with the use of teleconverters. So, for example the 500mm f/4, becomes f/5.6 with a 1x, and f/8 with the 2x. The Sigma Bigma becomes ~f/9 with a 1x, if it would even work, at 500mm. So for those using teleconverters, you've got to keep that in mind.
If you have, for example, the Nikkor AF 80-400mm f/4.5-5.6D ED VR, you know ahead of time you're safe as at its worst it's f/5.6, unless you use a teleconverter with it, which I don't. I have that lens, and I'll just think of it as f/5.6 for AF.