An update after the 2012 elections. Most Democratic county is on the left and most Republican on the right. * marks change from 2008.
Ohio: Cuyahoga / Mercer
Even after taking the most gop county slot in 08 (and the 06 midterms, fwiw), Mercer is still trending HARD gop, almost as much as any county outside coal country. Ironic considering as recent as 68 it trended hard Dem (see the election map that year; it's essentially the only county in thr western half of the state to go dem along with Montgomery and 'ucas).
On the other end of the spectrum, Monroe which was multiple times in recent Democratic county in the state went for Romney by a substantial margin.