The one that springs to mind is that the HOA-ARC tried to regulate where the satellite dishes could be mounted on the houses, but the owners prevailed, because the location if the dish affected reception. Another is that people succeeded in running low-density home day care (one or two other children besides their own) in spite of the HOA by-laws forbidding home-based businesses.
The HOA did succeed in having a high-density day care put out, but only because it was completely illegal in terms of the state-mandated safety provisions for chlldren, and was being run by renters, who had not secured permission in their lease.
Renters were a real problem altogether -- maybe 8 to 10% of the 150 attached houses. The HOA didn't allow renting for the first 6 years, but when the economy tanked when Obama came into office, people just couldn't sell, and the HOA started allowing it. Now that community is infested with Section 8'ers in the rental units.
location “of” the dish, not “if” the dish....
I'm just speculating here, but in the case of the low-density home care as you've described it, I suspect the owners prevailed against the HOA because the arrangement in question doesn't qualify is a "home-based business" by any objective measure. I'm actually surprised that the HOA even pushed to enforce that provision in an arrangement like that, because it sounds like the HOA rules as they were written could technically prohibit people from even hiring babysitters for their own children.