Here is a compilation of when each state permanently shifted relative allegiances. I apologize for the messy format. If the state only has a party, then it has remained relatively faithful to that party throughout its existence.:
Alaska: GOP
Hawaii: Dem
California: Dem since 1932, GOP since 1864
Oregon: Dem since 1972/56, GOP since 1944, Dem since 1932, GOP since 1872
Washington: Dem since 1968, GOP since 1960, Dem since 1932
Nevada: Dem since 2008, GOP since 1952, Dem since 1896
Arizona: GOP since 1952
New Mexico: Dem since 1988, GOP since 1956
Utah: GOP since 1952, Dem since 1916, GOP since 1904
Idaho: GOP since 1944/52, Dem since 1932, GOP since 1904
Colorado: GOP since 1924, Dem since 1896
Montana: GOP since 1952/60, Dem since 1896
Wyoming: GOP
Oklahoma: GOP since 1960
North Dakota: GOP since 1940,
South Dakota: GOP
Nebraska: GOP
Kansas: GOP
Minnesota: Dem since 1932
Iowa: Dem since 1972, GOP since 1856
Wisconsin: Dem since 1972, GOP since 1940, Dem since 1928, GOP since 1856
Missouri: GOP since 1996, Dem since 1988, GOP since 1972, Dem since 1948, GOP since 1940
Illinois: Dem since 1968, GOP since 1856/68
MIchigan: Dem since 1952, GOP since 1856
Indiana: GOP since 1928
Ohio: GOP since 1988, Dem since 1964, GOP since 1924, Dem since 1896
South Carolina: GOP since 1964, Dem since 1840
Georgia: GOP since 1964, Dem since 1844
North Carolina: GOP since 1964, Dem since 1856, Whig since 1840
Louisiana: GOP since 1964, Dem since 1860, Whig since 1848
Tennessee: GOP since 1960, Dem since 1872
Virginia: GOP since 1952
Florida: GOP since 1960
Kentucky: GOP since 1960/68, Dem since 1864
Arkansas: GOP since 1964
Mississippi: GOP since 1964
Alabama: GOP since 1964
Texas: GOP since 1972
Pennsylvania: Dem since 1952, GOP since 1872
Maryland: Dem since 1960, GOP since 1944, Dem since 1868
New Jersey: Dem since 1996, GOP since 1972, Dem since 1960/64, GOP since 1896, Dem since 1852
Delaware: Dem since 1992, GOP since 1964, Dem since 1940, GOP since 1928, Dem since 1904, GOP since 1892, Dem since 1856
West Virginia: GOP since 2000, Dem since 1936, GOP since 1892, Dem since 1872
New Hampshire: Dem since 1996, GOP since 1928, Dem since 1920, GOP since 1856, Dem since 1836
Maine: Dem since 1992, GOP since 1856, Dem since 1836
New York: Dem since 1960, GOP since 1892, Dem since 1860
Connecticut: Dem since 1960, GOP since 1948, Dem since 1940, GOP since 1892, Dem since 1864
Rhode Island: Dem since 1940, GOP since 1932, Dem since 1920
Massachusetts: Dem since 1944
Vermont: Dem since 1980
Or here is a prettier version: