Counties with the longest streak of voting for one party for President

[Nym90]

Idaho

D: Blaine (since 1988)
R: Clark (since 1932)

Illinois

D: Alexander, Cook, St. Clair (since 1972)
R: Edwards, Lee, Ogle (I in 1912, never D in the history of the Atlas which goes back to 1892)

Indiana

D: Lake (since 1972)
R: Hamilton, Hendricks (since 1912)

Iowa

D: Dubuque (since 1956)
R: Cass, Page (since 1932)

Kansas

D: Wyandotte (since 1972)
R: Doniphan (never D in Atlas history which goes back to 1888)

Kentucky

D: Elliott (Never R in Atlas history which dates to 1940)
R: Adair, Allen, Butler, Casey, Clay, Clinton, Cumberland, Edmonson, Grayson, Jackson, Laurel, Leslie, Lewis, McCreary, Monroe, Owsley, Pulaski, Rockcastle, Russell (never D in continuous Atlas history which goes back to 1940, although Jackson and McCreary voted I in 1912 and Adair, Allen, Casey, Edmonson, Grayson, Laurel and Pulaski voted D in 1912)

Louisiana

D: East Carroll, Iberville, Madison, Orleans, St. Helena, St. James (since 1972)
R: Bossier, Jefferson, Lafayette, La Salle, Ouachita, St. Tammany, Union (since 1968 when all voted I. Bossier has the longest streak of not voting D, having last went D in 1944)

[Nym90]

Maine

D: Androscoggin, Aroostook, Cumberland, Franklin, Hancock, Kennebec, Knox, Oxford, Sagadohoc, York (since 1988)
R: Piscataquis (since 1996)

Maryland

D: Baltimore City (since 1956), Prince George's (since 1972)
R: Garrett (since 1912 when it voted I, hasn't voted D in Atlas history which dates to 1900)

Massachusetts

D: Suffolk (since 1924)
R: None. The last time any counties went R were Barnstable, Plymouth, and Worcester in 1988.

Michigan

D: Wayne (since 1928)
R: Missaukee, Ottawa, Sanilac (since 1912 when they all voted I, and none have gone D in Atlas history which dates to 1884)

Minnesota

D: Ramsey (since 1924)
R: Carver, Otter Tail (since 1932)

Mississippi

D: Claiborne, Holmes, Jefferson (since 1964)
R: Choctaw, Clarke, Forrest, Franklin, Harrison, Jackson, Jones, Lamar, Lauderdale, Lincoln, Lowndes, Newton, Rankin, Scott, Simpson, Smith (since 1968 when all voted I, though Clarke was a tie in 1980). Forrest has the longest streak of not voting D, having not done so since 1944.

Missouri

D: St. Louis City (since 1924), Jackson (since 1972)
R: Gasconade, Putnam, Taney (never D in Atlas history which dates to 1888)

Montana

D: Deer Lodge (since 1924)
R: Beaverhead, Fallon, Powder River, Stillwater, Sweet Grass (since 1936)

[Nym90]

Nebraska

D: Thurston (since 2000)
R: Keya Paha (since 1916)

Nevada

D: Clark (since 1988)
R: Douglas (since 1936)

New Hampshire

D: Cheshire, Grafton, Merrimack, Strafford (since 1988)
R: Belknap, Carroll, Rockingham (since 2008)

New Jersey

D: Essex (since 1972)
R: Hunterdon, Morris, Sussex, Warren (since 1964)

New Mexico

D: Rio Arriba, San Miguel (since 1956)
R: Lincoln (since 1936)

New York

D: Bronx, Kings, New York (since 1924). Outside of NYC it would be Albany and Erie, both since 1972.
R: Allegany, Genesee, Greene, Hamilton, Livingston, Orleans, Putnam, Steuben, Tioga, Wayne, Wyoming (since 1964)

North Carolina

D: Northampton (Never R in Atlas history which dates to 1924)
R: Avery, Mitchell, Wilkes, Yadkin (Never D in Atlas history dating to 1924, though Avery, Mitchell, and Wilkes voted I in 1912)

North Dakota

D: Rolette (since 1952)
R: Golden Valley, Grant, Kidder, Logan, McIntosh, Mercer, Sheridan (since 1936)

Ohio

D: Cuyahoga, Mahoning, Trumbull (since 1972)
R: Delaware (since 1916)

Oklahoma

D: None (Cherokee, Choctaw, Haskell, Hughes, Latimer, McIntosh, Muskogee, Okmulgee, Ottawa all voted D in 2000, the last time any county voted D)
R: Major (since 1932)

Oregon

D: Columbia (since 1928)
R: Josephine (since 1936)

Pennsylvania

D: Philadelphia (since 1932)
R: Snyder, Union, Wayne (since 1912 when all voted I, Snyder and Union haven't voted D in Atlas history which dates to 1888)

Rhode Island

D: Providence (since 1972)
R: None (Bristol, Kent, Newport, and Washington voted R in 1984, the last time any county voted R)

[Nym90]

South Carolina

D: Allendale, Clarendon, Fairfield, Hampton, Jasper, Lee, McCormick, Marion, Marlboro, Orangeburg, Williamsburg (since 1972)
R: Aiken (since 1952)

South Dakota

D: Shannon (since 1952)
R: Lawrence (since 1916)

Tennessee

D: Haywood (since 1972)
R: Cocke, Hancock, Wayne (Never D in Atlas history which dates to 1912)

Texas

D: Brooks, Duval, Jim Hogg, Maverick, Starr, Webb, Zapata (never R in consecutive Atlas history which dates to 1940, though Webb and Zapata voted R in 1912)
R: Kendall (Never D in Atlas history which dates to 1940, though it voted I in 1912)

Utah

D: None. Grand, Salt Lake and Summit were the last to vote D in 2008.
R: Garfield, Iron, Kane, San Juan, Sanpete, Sevier (since at least 1936 for which no data exists, Garfield, Iron, Kane, and San Juan otherwise have the longest streak having voted R since 1916)

Vermont

D: Addison, Chittenden, Franklin, Grand Isle, Windham (since 1984)
R: None. The last to vote R was Essex in 2004.

Virginia

D: Charles City (since 1956)
R: Floyd (never D in Atlas history which dates to 1932, though it voted I in 1912)

Washington

D: Grays Harbor (since 1928)
R: Adams (since 1936)

West Virginia

D: None. Boone, Braxton, Jefferson, Marion, McDowell, Monongalia and Webster were the last to vote D in 2008.
R: Morgan (never in Atlas history which dates to 1912)

Wisconsin

D: Douglas (since 1928)
R: Walworth (since 1912).

Wyoming

D: Teton (since 2000)
R: Crook, Johnson (since 1932)

[Nym90]

Updated for 2016:

Alabama

D: Greene, Macon, Sumter (Greene and Sumter voted R in 1964, Macon voted I in 1964, R in 1956)
R: Baldwin, Houston, Lee, Mobile, Shelby (All voted I in 1968, Baldwin, Mobile, and Shelby last voted D in 1952 which is the longest streak of not voting D, though all three voted D/I in 1960, so Houston can make an argument, having last voted D in 1956, but R in 1960).

Arizona

D: Apache (since 1980)
R: Maricopa, Yavapai (since 1948)

Arkansas

D: Chicot, Desha, Jefferson, Lee, Phillips (since 1972)
R: Benton, Sebastian (since 1948)

California

D: Yolo (since 1952)
R: Sutter (since 1940)

Colorado

D: Costilla (since 1924)
R: Elbert (since 1932)

Connecticut

D: Hartford (since 1984)
R: Litchfield (since 2008)

Delaware

D: New Castle (since 1988)
R: Sussex (since 1996)

Florida

D: Gadsden (since 1972)
R: Indian River, Lake, Lee, Manatee, Martin, Sarasota (since 1944)

Georgia

D: Calhoun, Clay, Fulton, Hancock, Macon, Stewart, Talbot, Taliaferro, Warren (since 1972)
R: Catoosa, Columbia, Dade, Fannin, Fayette, Lee, Lowndes, Walker (since 1976)

Hawaii

D: Hawaii, Honolulu, Kauai, Maui (since 1984)
R: None (Hawaii, Honolulu, Kauai, and Maui all voted R in 1984, the last time any county voted R)

[Nym90]

Idaho

D: Blaine (since 1988)
R: Clark (since 1932)

Illinois

D: Cook, St. Clair (since 1972)
R: Edwards, Lee, Ogle (I in 1912, never D in the history of the Atlas which goes back to 1892)

Indiana

D: Lake (since 1972)
R: Hamilton, Hendricks (since 1912)

Iowa

D: Johnson (since 1960)
R: Cass, Page (since 1932)

Kansas

D: Wyandotte (since 1972)
R: Doniphan (never D in Atlas history which goes back to 1888)

Kentucky

D: Jefferson (since 1988)
R: Adair, Allen, Butler, Casey, Clay, Clinton, Cumberland, Edmonson, Grayson, Jackson, Laurel, Leslie, Lewis, McCreary, Monroe, Owsley, Pulaski, Rockcastle, Russell (never D in continuous Atlas history which goes back to 1940, although Jackson and McCreary voted I in 1912 and Adair, Allen, Casey, Edmonson, Grayson, Laurel and Pulaski voted D in 1912)

Louisiana

D: East Carroll, Iberville, Madison, Orleans, St. Helena, St. James (since 1972)
R: Bossier, Jefferson, Lafayette, La Salle, Ouachita, St. Tammany, Union (since 1968 when all voted I. Bossier has the longest streak of not voting D, having last went D in 1944)

[Nym90]

Maine

D: Cumberland, Hancock, Knox, Sagadohoc, York (since 1988)
R: Piscataquis (since 1996)

Maryland

D: Baltimore City (since 1956). Among counties the longest streak is Prince George's (since 1972)
R: Garrett (since 1912 when it voted I, hasn't voted D in Atlas history which dates to 1900)

Massachusetts

D: Suffolk (since 1924)
R: None. The last time any counties went R were Barnstable, Plymouth, and Worcester in 1988.

Michigan

D: Wayne (since 1928)
R: Missaukee, Ottawa, Sanilac (since 1912 when they all voted I, and none have gone D in Atlas history which dates to 1884)

Minnesota

D: Ramsey (since 1924)
R: Carver, Otter Tail (since 1932)

Mississippi

D: Claiborne, Holmes, Jefferson (since 1964)
R: Choctaw, Clarke, Forrest, Franklin, Harrison, Jackson, Jones, Lamar, Lauderdale, Lincoln, Lowndes, Newton, Rankin, Scott, Simpson, Smith (since 1968 when all voted I, though Clarke was a tie in 1980). Forrest has the longest streak of not voting D, having not done so since 1944.

Missouri

D: St. Louis City (since 1924). Among counties the longest streak is Jackson (since 1972)
R: Gasconade, Putnam, Taney (never D in Atlas history which dates to 1888)

Montana

D: Deer Lodge (since 1924)
R: Beaverhead, Fallon, Powder River, Stillwater, Sweet Grass (since 1936)

[Nym90]

Nebraska

D: Douglas, Lancaster (since 2012)
R: Keya Paha (since 1916)

Nevada

D: Clark (since 1988)
R: Douglas (since 1936)

New Hampshire

D: Cheshire, Grafton, Merrimack, Strafford (since 1988)
R: Belknap, Carroll, Rockingham (since 2008)

New Jersey

D: Essex (since 1972)
R: Hunterdon, Morris, Sussex, Warren (since 1964)

New Mexico

D: Rio Arriba, San Miguel (since 1956)
R: Lincoln (since 1936)

New York

D: Bronx, Kings, New York (since 1924). Outside of NYC it would be Albany and Erie, both since 1972.
R: Allegany, Genesee, Greene, Hamilton, Livingston, Orleans, Putnam, Steuben, Tioga, Wayne, Wyoming (since 1964)

North Carolina

D: Northampton (Never R in Atlas history which dates to 1924)
R: Avery, Mitchell, Wilkes, Yadkin (Never D in Atlas history dating to 1924, though Avery, Mitchell, and Wilkes voted I in 1912)

North Dakota

D: Rolette (since 1952)
R: Golden Valley, Grant, Kidder, Logan, McIntosh, Mercer, Sheridan (since 1936)

Ohio

D: Cuyahoga, Mahoning (since 1972)
R: Delaware (since 1916)

Oklahoma

D: None (Cherokee, Choctaw, Haskell, Hughes, Latimer, McIntosh, Muskogee, Okmulgee, Ottawa all voted D in 2000, the last time any county voted D)
R: Major (since 1932)

Oregon

D: Clatsop (since 1956)
R: Josephine (since 1936)

Pennsylvania

D: Philadelphia (since 1932)
R: Snyder, Union, Wayne (since 1912 when all voted I, Snyder and Union haven't voted D in Atlas history which dates to 1888)

Rhode Island

D: Providence (since 1972)
R: Kent (since 2012)

[Nym90]

South Carolina

D: Allendale, Clarendon, Fairfield, Hampton, Jasper, Lee, Marion, Marlboro, Orangeburg, Williamsburg (since 1972)
R: Aiken (since 1952)

South Dakota

D: Oglala Lakota (since 1952)
R: Lawrence (since 1916)

Tennessee

D: Haywood (since 1972)
R: Cocke, Hancock, Wayne (Never D in Atlas history which dates to 1912)

Texas

D: Brooks, Duval, Jim Hogg, Maverick, Starr, Webb, Zapata (never R in consecutive Atlas history which dates to 1940, though Webb and Zapata voted R in 1912)
R: Kendall (Never D in Atlas history which dates to 1940, though it voted I in 1912)

Utah

D: Salt Lake, Summit (since 2012)
R: Kane (since 1916)

Vermont

D: Addison, Chittenden, Franklin, Grand Isle, Windham (since 1984)
R: Essex (since 2012)

Virginia

D: Charles City (since 1956)
R: Floyd (never D in Atlas history which dates to 1932, though it voted I in 1912)

Washington

D: Jefferson (since 1980)
R: Adams (since 1936)

West Virginia

D: None. Boone, Braxton, Jefferson, Marion, McDowell, Monongalia and Webster were the last to vote D in 2008.
R: Morgan (never in Atlas history which dates to 1912)

Wisconsin

D: Douglas (since 1928)
R: Walworth (since 1912).

Wyoming

D: Teton (since 2000)
R: Crook, Johnson (since 1932)

[Nym90]

Tennessee

D: Haywood (since 1972)
R: Cocke, Hancock, Wayne (Never D in Atlas history which dates to 1912)

According to the maps on the Wikipedia pages for each election, Wayne has been R since 1876.  Cocke and Hancock have been R since 1868.  Hancock did vote for Breckenridge in 1860 but the last time Cocke voted Democrat was for Andrew Jackson in 1832, and even that appears to be by a close margin.

Thanks Don. I've stuck to using official Atlas data for this thread (though I jumped the gun a bit this year and used the AP for county results Dave doesn't have posted yet).

[Nym90]

Thanks Gmantis.