How do I fix a squeaky/whiny ceiling fan?
Seems to me that it would depend on where the squeak is coming from.

If it;s inside the mechanism, or somewhere where parts of the fan are rubbing tegether then some WD-40 would probably fix it right up, but if the whole mounting is wobbling and causing the mount to rub against the junction box then you might try tightening the mounting hardware or shimmiing it out with something to make the mounting tighter.