Top Dem and Rep results, by state

[GMantis]

An update after the 2012 elections. Most Democratic county is on the left and most Republican on the right. * marks change from 2008.

Alabama: Macon / Blount
Arizona: Santa Cruz / Mohave*
Arkansas: Phillips / Polk*
California: San Francisco / Modoc
Colorado: Denver* / Cheyenne
Connecticut: Hartford / Litchfield
Delaware: New Castle / Sussex
Florida: Gadsden / Holmes
Georgia: Clayton / Banks*
Hawaii: Hawaii* / Honolulu
Idaho: Blaine / Madison
Illinois: Cook / Wayne*
Indiana: Lake / Kosciusko
Iowa: Johnson / Sioux
Kansas: Wyandotte / Sheridan*
Kentucky: Jefferson* / Leslie*
Louisiana: Orleans / La Salle
Maine: Cumberland / Piscataquis
Maryland: Prince George / Garrett
Massachusetts: Suffolk / Plymouth
Michigan: Wayne / Ottawa
Minnesota: Ramsey / Wadena*
Mississippi: Jefferson / George
Missouri: Saint Louis City / Osage*
Montana: Glacier / Garfield
Nebraska: Thurston / Grant
Nevada: Clark / Eureka
New Hampshire: Cheshire* / Belknap*
New Jersey: Essex / Sussex
New Mexico: Taos / Lea
New York: Bronx / Wyoming*
North Carolina: Durham / Yadkin
North Dakota: Sioux / Billings
Ohio: Cuyahoga / Mercer
Oklahoma: Cherokee / Cimarron*
Oregon: Multnomah / Lake
Pennsylvania: Philadelphia / Fulton
Rhode Island: Providence / Washington*
South Carolina: Allendale / Pickens
South Dakota: Shannon / Harding*
Tennessee: Shelby / Wayne*
Texas: Starr / King
Utah: Summit / Rich*
Vermont: Windham / Essex
Virginia: Petersburg / Tazewell*
Washington: King* / Garfield
West Virginia: Jefferson* / Grant
Wisconsin: Menominee / Washington
Wyoming: Teton / Campbell*

Interestingly the most Republican counties are those that have changed most.

[GMantis]

I was thinking the most Dem county in TX was Travis.

There were 15 more Democratic counties this year, though since most are small ones in the Rio Grande valley, they are often overlooked.

[GMantis]

I was thinking the most Dem county in TX was Travis.

There were 15 more Democratic counties this year, though since most are small ones in the Rio Grande valley, they are often overlooked.

I wonder why they're overlooked, is it because no one there speaks English?

Yes, basically. All of those counties are almost entirely Hispanic, Spanish speaking and quite poor. They also have rather low turnout.

[GMantis]

Leslie is the easternmost of the superheavily Republican south central kentucky counties, abutting the sothern coalfield counties that have swung against the Dems so very, very hard (and begun to do so before the northern part. Oh, and thus restored the pre-New Deal pattern for a fleeting moment in 04, these places also having old Unionist Republican traditions. Although what mattered more is their strong Evangelical tradition. Though the issue is related. End of weird aside.) So they took part in that swing a bit and usurped Jackson County's traditional place? That's actually funny.

It seems that Leslie is also a coal producing county (see map) though not nearly as the counties to its east. Which probably explains why it took part in this year's swing. Strange though why it was so Republican when coal counties in Kentucky were reliably Democratic. Perhaps coal production started relatively recently?
Incidentally, Elliott county is not a big producer of coal. Perhaps this is why it still voted Democratic this time.

[GMantis]

Hmmm. If coal mining started late, like after the mass introduction of cars, it wouldn't have much of an effect (since miners wouldn't necessarily live in the county). But the county's population rose massively in the 30s (though, again, not that massively), dropped like a stone in the 50s, rose again in the 70s. That looks like the coalfield might have opened in the 30s. It appears to have never been unionized, though.

Also
http://en.wikipedia.org/wiki/Hurricane_Creek_mine_disaster
http://www.usmra.com/saxsewell/finley.htm

The population profile is similar to the neighboring, also ultra-Republican Clay county, which along with Leslie was described by the New York Times in 1970 as having no economy other than coal.

[GMantis]

An update after the 2016 election. Most Democratic county is on the left and most Republican on the right. * marks change from 2012.

Alabama: Macon / Winston*
Arizona: Santa Cruz / Mohave
Arkansas: Phillips / Polk
California: San Francisco / Lassen*
Colorado: Denver / Kiowa*
Connecticut: Hartford / Litchfield
Delaware: New Castle / Sussex
Florida: Gadsden / Holmes
Georgia: Clayton / Glascock*
Hawaii: Maui* / Honolulu
Idaho: Blaine / Idaho*
Illinois: Cook / Wayne
Indiana: Monroe* / Daviess*
Iowa: Johnson / Lyon*
Kansas: Douglas* / Wallace*
Kentucky: Jefferson / Leslie
Louisiana: Orleans / La Salle
Maine: Cumberland / Piscataquis
Maryland: Prince George / Garrett
Massachusetts: Suffolk / Plymouth
Michigan: Washtenaw* / Missaukee*
Minnesota: Ramsey / Morrison*
Mississippi: Claiborne* / George
Missouri: Saint Louis City / Mercer*
Montana: Glacier / Garfield
Nebraska: Douglas* / Hayes*
Nevada: Clark / Eureka
New Hampshire: Grafton* / Belknap
New Jersey: Essex / Ocean*
New Mexico: Santa Fe* / Catron*
New York: Bronx / Wyoming
North Carolina: Durham / Graham*
North Dakota: Sioux / Burke*
Ohio: Cuyahoga / Mercer
Oklahoma: Oklahoma* / Cimarron
Oregon: Multnomah / Lake
Pennsylvania: Philadelphia / Fulton
Rhode Island: Providence / Kent*
South Carolina: Allendale / Pickens
South Dakota: Oglala Lakota / Harding
Tennessee: Shelby / Wayne
Texas: Starr / Roberts*
Utah: Summit / Piute*
Vermont: Chittenden* / Essex
Virginia: Petersburg / Bland*
Washington: King / Lincoln*
West Virginia: Monongalia* / Grant
Wisconsin: Menominee / Florence*
Wyoming: Teton / Crook*

Oglala Lakota county was named Shannon before 2015.

Some notable most Democratic/Republican county streaks: Madison county, most Republican in Idaho since 1976 (though it did became McMullin's best county this time around), Lake county - most Democratic in Indiana since 1984, Ottawa - most Republican in Michigan since 1976 (it has now fallen to 31st place), Wayne - most Democratic in Michigan all but two times (1976 and 1984) since 1960, Sioux - most Republican in Iowa since at least 1956 and Wyandotte - most Democratic in Kansas since 1968.

[GMantis]

An update after the 2016 election. Most Democratic county is on the left and most Republican on the right. * marks change from 2012.
...

Some notable most Democratic/Republican county streaks: Madison county, most Republican in Idaho since 1976 (though it did became McMullin's best county this time around), Lake county - most Democratic in Indiana since 1984, Ottawa - most Republican in Michigan since 1976 (it has now fallen to 31st place), Wayne - most Democratic in Michigan all but two times (1976 and 1984) since 1960, Sioux - most Republican in Iowa since at least 1956 and Wyandotte - most Democratic in Kansas since 1968.

Sioux/Lyon, IA is a case of the former having higher conservative third-party vote. If add McMullin to Trump, Madison, ID is beaten out by Franklin.

For the sake of consistency, I'm following the criteria used by Lewis: highest percentage, not margin.

[GMantis]

I'm going to try Michigan since 1960.  Most D county is in red, most R county is in blue, and the election year is colored for the statewide winner:

1960: Wayne (66.0%) Missaukee (79.8%)
1964: Wayne (76.0%) Missaukee (58.1%)
1968: Wayne (63.2%) Missaukee (67.7%)
1972: Sanilac (72.9%) Wayne (53.3%)
1976: Ottawa (74.1%) Gogebic (61.0%)
1980: Ottawa (67.9%) Wayne (51.2%)
1984: Ottawa (79.7%) Gogebic (58.0%)
1988: Ottawa (76.2%) Wayne (60.2%)
1992: Wayne (60.4%) Ottawa (59.1%)
1996: Wayne (69.0%) Ottawa (64.4%)
2000: Wayne (69.0%) Ottawa (71.2%)
2004: Wayne (69.4%) Ottawa (71.6%)
2008: Wayne (74.0%) Ottawa (61.0%)
2012: Wayne (72.8%) Ottawa (66.4%)
2016: Missaukee (73.6%) Washtenaw (67.6%)

Extending this series back as far as this source has information:

1956: Sanilac (78.9%) Wayne (57.9%)
1952: Sanilac (82.5%) Wayne (57.4%)
1948: Sanilac (77.7%) Wayne (57.9%)
1944: Wayne (63.4%) Sanilac (82.1%)
1940: Sanilac (82.1%) Alger (63.8%)
1936: Genesee (67.5%) Sanilac (63.2%)
1932: Macomb (63.7%) Keweenaw (72.5%)
1928: Missaukee (87.2%) Delta (49.6%)
1924: Keweenaw (91.2%) Monroe (32.4%)
1920: Keweenaw (90.2%) Manistee (47.8%)
1916: Keweenaw (76.6%) Kent (53.7%)
1912: Iron (45.2%) Mackinac (41.3%)
1864: Grand Traverse (81.9%) Mackinac (86.1%)
1860: Midland (78.5%) Emmet (84.9%)
1856: Midland (78.5%) Sanilac (79.9%)

Roosevelt's best county in 1912 was Muskegon (52.3%). LaFollette's best county was Delta (44%).

[GMantis]

An update after the 2020 election. Most Democratic county is on the left and most Republican on the right. * marks change from 2016.

Alabama: Macon / Winston
Arizona: Santa Cruz / Mohave
Arkansas: Pulaski* / Searcy*
California: San Francisco / Lassen
Colorado: Denver / Kiowa
Connecticut: Hartford / Litchfield
Delaware: New Castle / Sussex
Florida: Gadsden / Holmes
Georgia: Clayton / Brantley*
Hawaii: Hawaii* / Honolulu
Idaho: Blaine / Bear Lake*
Illinois: Cook / Wayne
Indiana: Marion* / Franklin*
Iowa: Johnson / Lyon
Kansas: Douglas / Wallace
Kentucky: Fayette* / Leslie
Louisiana: Orleans / Cameron*
Maine: Cumberland / Piscataquis
Maryland: Prince George / Garrett
Massachusetts: Suffolk / Bristol*
Michigan: Washtenaw / Missaukee
Minnesota: Ramsey / Morrison
Mississippi: Jefferson* / George
Missouri: Saint Louis City / Mercer
Montana: Glacier / Garfield
Nebraska: Douglas / Grant*
Nevada: Clark / Eureka
New Hampshire: Grafton / Belknap
New Jersey: Essex / Ocean
New Mexico: Taos* / Lea*
New York: New York* / Wyoming
North Carolina: Durham / Yadkin*
North Dakota: Sioux / Slope*
Ohio: Cuyahoga / Holmes*
Oklahoma: Oklahoma / Cimarron
Oregon: Multnomah / Lake
Pennsylvania: Philadelphia / Fulton
Rhode Island: Newport* / Kent
South Carolina: Allendale / Pickens
South Dakota: Oglala Lakota / Harding
Tennessee: Davidson* / Scott*
Texas: Travis* / Roberts
Utah: Summit / Piute
Vermont: Chittenden / Essex
Virginia: Petersburg / Lee*
Washington: King / Lincoln
West Virginia: Monongalia / Grant
Wisconsin: Menominee / Florence
Wyoming: Teton / Crook

Not as many drastic changes as last time, though it's certainly notable that for the first time since before 1960 the best Democratic county in Texas was not one of three in the Rio Grande valley (Duval, Starr and Zavala), but Travis instead.