Most people (ballet dancers, for instance) reduce the feeling of dizziness by "spotting." Evidently snapping the head around and focussing on the next spot helps to mitigate the confusion coming to the brain from the inner ear. Figure skaters somehow train themseves to spin without spotting, yet without getting dizzy.
The only top skater who spotted, as far as I know, was Kevin Van Der Perren -- this slowed him down a tad and made it harder to get in the rotations in a jump. Although he did have a quad and in fact was the first skater to do a 4-3-3 combination. I don't know about his spins.
Interesting that Michelle Kwan was mentioned. Michelle was not a fast spinner (nor a very flexible one), and as for spinning in both directions, this didn't really work out for her and she dropped it from her programs after a couole of seasons.
Sychonized swimmers can literally hold their breath until they pass out (bratty children may threaten to do this, but they can't, really)

) Sword swallowers can suppress the gag reflex. Fascinating study.