Below is a alphabetical index of Ohio Governors.  In addition to births and deaths, the statewide and federal elected positions they held are listed.  The links will take you to biographies courtesy of the Ohio Historical Society.

Allen, William
b. 1803 d. 1879
Congress 1832-1834
U.S. Senate 1837-1849
Governor 1974-1878

Anderson, Charles
b. 1814 d. 1895
Ohio Senate 1945-1849
Ohio Governor 1865-1866

Bartley, Mordecai
b. 1783 d. 1870
Ohio Senate 1817-1818
Congress 1823-1831
Governor 1844-1846

Bartley, Thomas
b. 1812 d. 1885
Ohio House 1839-1845
Governor 1844
Ohio Supreme Court 1852-1859

Bebb, William
b. 1802 d. 1873
Governor 1846-1849

Bishop, Richard
b. 1812 d. 1893
Mayor, Cincinnati 1859-1861
Governor 1878-1880

Bricker, John
b. 1893 d. 1986
Ohio Attorney General 1932-1939
Governor 1939-1945
U.S. Senate 1947-1959

Brough, John
b. 1811 d. 1865
Oho House 1839-1839
Ohio Auditor 1839-1845
Governor 1863-1865

Brown, Ethan
b. 1776 d. 1852
Ohio Supreme Court 1810-1818
Governor 1818-1822
U.S. Senate 1822-1825
Indiana House 1841-1843

Brown, John
b. 1913 d. 1993
Medina Mayor 1950-1952
Ohio Lt. Governor 1952-1957; 1963-1975
Governor 1957
Ohio House 1959-1960
Ohio Senate 1961-1963

Bushnell, Asa
b. 1934 d. 1904
Governor 1896-1900

Campbell, James
b. 1843 d. 1924
U.S. Congress 1883-1889
Governor 1890-1892

Celeste, Richard
b. 1937
Ohio House 1971-1975
Ohio Lt. Governor 1975-1979
Governor 1983-1991

Chase, Salmon
b. 1808 d. 1873
U.S. Senate 1850-1855; 1860
Governor 1855-1859

Corwin, Thomas
b. 1794 d. 1865
Ohio House 1821-1823; 1829-1830
U.S. Congress 1831-1840; 1859-1861
Governor 1840-1842
U.S. Senate 1845-1850

Cooper, Myers
b. 1873 d. 1958
Governor 1929-1931

Cox, Jacob
b. 1828 d. 1900
Ohio Senate 1859-1861
Governor 1866-1868
U.S. Congress 1877-1879

Cox, James
b. 1870 d. 1957
U.S. Congress 1909-1913
Governor 1913-1915; 1917-1921

Davey, Martin
b. 1884 d. 1946
Kent Mayor 1914-1918
U.S. Congress 1918-1929
Governor 1935-1939

Davis, Harry
b. 1878 d. 1950
Cleveland Mayor 1915-1920; 1933-1935
Governor 1921-1923

Dennison, William
b. 1815 d. 1882
Ohio Senate 1848-1852
Governor 1860-1862

DiSalle, Michael
b. 1908 d. 1981
Ohio House 1937-1939
Governor 1959-1963

Donahey, Vic
b. 1873 d. 1946
Ohio Auditor 1913-1921
Governor 1923-1929
U.S. Senate 1935-1941

Foraker, Joseph
b. 1846 d. 1917
Governor 1885-1889
U.S. Senator 1897-1909

Ford, Seabury
b. 1801 d. 1855
Ohio House 1835-1841
Ohio Senate 1841-1848
Governor 1849-1850

Foster, Charles
b. 1828 d. 1904
U.S. House 1871-1879
Governor 1880-1884

Gilligan, John
b. 1921 d. 2013
U.S. House 1965-1967
Governor 1971-1975

Harmon, Judson
b. 1846 d. 1927
Governor 1909-1913

Harris, Andrew
b. 1835 d. 1915
Ohio Senate 1866-1870
Ohio Lt. Governor 1891-1895; 1905-1906
Governor 1906-1909

Hayes, Rutherford
b. 1822 d. 1893
U.S. House 1865-1867
Governor 1868-1872; 1876
U.S. President 1877-1881

Herbert, Thomas
b. 1894 d. 1974
Ohio Attorney General 1939-1945
Governor 1947-1949
Ohio Supreme Court 1957-1963

Herrick, Myron
b. 1854 d. 1929
Governor 1904-1906

Hoadly, George
b. 1826 d. 1902
Governor 1884-1886

Hollister, Nancy
b. 1949
Ohio Lt. Governor 1995-1998
Governor 1998-1999
Ohio House 1999-2005

Huntington, Samuel
b. 1765 d. 1817
Ohio Supreme Court 1803-1808
Governor 1808-1810

Kasich, John
b. 1952
Ohio Senate 1979-1983
U.S. House 1983-2001
Governor 2011-present

Kirker, Thomas
b. 1760 d. 1837
Ohio House 1803; 1816-1817
Ohio Senate 1803-1807; 1809-1815; 1821-1825
Governor 1807-1808

Lausche, Frank
b. 1895 d. 1990
Cleveland Mayor 1942-1944
Governor 1945-1947; 1949-1957
U.S. Senate 1957-1969

Looker, Othniel
b. 1757 d. 1845
Ohio House 1807-1809
Ohio Senate 1810-1812; 1813-1817
Governor 1814

Lucas, Robert
b. 1781 d. 1853
Ohio House 1810-1812; 1831-1832
Ohio House 1814-1822; 1824-1828; 1829-1830
Governor 1832-1836

McArthur, Duncan
b. 1772 d. 1839
Ohio Senate 1805-1812; 1821-1823; 1829-1830
Ohio House 1815-1819; 1826-1827
U.S. House 1823-1825
Governor 1830-1832

McKinley, William
b. 1843 d. 1901
U.S. House 1877-1884; 1885-1891
Governor 1892-1896
U.S. President 1897-1901

Medill, William
b. 1802 d. 1865
Ohio House 1835-1839
U.S. House 1839-1843
Ohio Lt. Governor 1852-1853
Governor 1853-1855

Meigs, Return Jonathan
b. 1765 d. 1824
Ohio Supreme Court 1803-1804
U.S. Senate 1808-1810
Governor 1810-1814

Morrow, Jeremiah
b. 1771 d. 1852
Territorial House of Representative
Territorial Senate
Delegate, 1802 Constitutional Convention
Ohio Senate 1803
U.S. House 1803-1813; 1840-1843
U.S. Senate 1813-1819
Governor 1822-1826

Nash, George
b. 1842 d. 1904
Ohio Attorney General 1880-1883
Ohio Supreme Court 1883-1885
Governor 1900-1904

Noyes, Edward
b. 1832-1890
Governor 1872-1874

O'Neill, C. William
b. 1916 d. 1978
Ohio House 1939-1950
Ohio Attorney General 1951-1957
Governor 1957-1959
Ohio Supreme Court 1961-1978

Pattison, John
b. 1847 d. 1906
Ohio House 1873-1875
Ohio Senate 1890-1891
U.S. House 1891-1893
Governor 1905-1906

Rhodes, James
b. 1909 d. 2001
Columbus Mayor 1944-1952
Ohio Auditor 1953-1963
Ohio Governor 1963-1971; 1975-1983

Shannon, Wilson
b. 1802 d. 1877
Governor 1838-1840; 1842-1844
U.S. House 1853-1855

Strickland, Ted
b. 1941
U.S. House 1993-1995; 1997-2007
Governor 2007-2011

Taft, Robert
b. 1942
Ohio House 1977-1981
Ohio Secretary of State 1991-1999
Governor 1999-2007

Tiffin, Edward
b. 1766 d. 1829
Governor 1803-1807
U.S. Senate 1807-1809
Ohio House 1809-1812

Tod, David
b. 1805 d. 1868
Ohio Senate 1838-1840
Governor 1862-1864

Trimble, Allen
b. 1783 d. 1870
Ohio House 1815-1816
Ohio Senate 1816-1822; 1822-1826
Governor 1822; 1826-1830

Vance, Joseph
b. 1786 d. 1852
Ohio House 1812-1814; 1815-1816; 1819-1820
U.S. House 1821-1835; 1843-1847
Governor 1836-1838
Ohio Senate 1839-1841

Voinovich, George
b. 1936
Ohio House 1967-1971
Ohio Lt. Governor 1979
Cleveland Mayor 1979-1986
Ohio Governor 1991-1999
U.S. Senate 1999-2011

White, George
b. 1872 d. 1953
Ohio House 1902-1908
U.S. House 1911-1915; 1917-1919
Governor 1931-1935

Willis, Frank
b. 1871 d. 1928
Ohio House 1900-1904
U.S. House 1911-1915
Governor 1915-1917
U.S. Senate 1921-1928

Wood, Reuben
b. 1792 d. 1864
Ohio Senate 1825-1830
Ohio Supreme Court 1833-1847
Governor 1850-1853

Worthington, Thomas
b. 1773 d. 1827
Ohio House 1803; 1807-1809; 1820-1824
U.S. Senate 1803-1807; 1811-1814
Governor 1814-1818

Young, Thomas
b. 1832 d. 1888
Ohio House 1865-1867
Ohio Senate 1871-1873
Ohio Lt. Governor 1875-1877
Governor 1877
U.S. House 1879-1883

Below is an index of Ohio Governors by term.  The links will take you to biographies courtesy of the Ohio Historical Society.

Key: DR: Democratic Republican; F: Federalist; D: Democrat; W: Whig;
UL: Union League; R: Republican; U: Union

Edward Tiffin (DR)
March 3, 1803-March 4, 1807

Thomas Kirker (acting) (DR)
March 4, 1807-December 12, 1808
(Tiffin offered governorship, declined.  Return J. Meigs elected, but disqualified.  Nathaniel Massie named Governor, but declined

Samuel Huntington (DR)
December 12, 1808-December 8, 1810

Return Jonathan Meigs Jr. (DR)
December 12, 1810-March 24, 1814

Othniel Looker (acting) (F)
March 24, 1814-December 8, 1814

Thomas Worthington (DR)
December 8, 1814-December 12, 1818

Ethan A. Brown (DR)
December 14, 1818-January 4, 1822

Allen Trimble (acting) (F)
January 4, 1822-December 28, 1822

Jeremiah Morrow (DR)
December 28, 1822-December 19, 1826

Allen Trimble (F)
December 19, 1826-December 18, 1830

Duncan McArthur (DR)
December 18, 1830-December 7, 1832

Robert Lucas (D)
December 7, 1832-December 12, 1836

Joseph Vance (W)
December 12, 1836-December 13, 1838

Wilson Shannon (D)
December 13, 1838-December 16, 1840

Thomas Corwin (W)
December 16, 1840-December 14, 1842

Wilson Shannon (D)
December 14, 1842-April 15, 1844

Thomas W. Bartley (acting) (D)
April 15, 1844-December 3, 1844

Mordecai Bartley (W)
December 3, 1844-December 12, 1846

William Bebb (term extended) (W)
December 12, 1846-January 22, 1849

Seabury Ford (W)
January 22, 1849-December 12, 1850

Reuben Wood (D)
December 12, 1850-July 13, 1853

William Medill (acting/elected) (D)
July  13, 1853-January 14, 1856

Salmon P. Chase (R)
January 14, 1856-January 9, 1860

William Dennison Jr. (R)
January 9, 1860-January 13, 1862

David Tod (UL)
January 13, 1862-January 11, 1864

John Brough (UL)
January 11, 1864-August 29, 1865

Charles Anderson (acting) (UL)
August 29, 1865-January 8, 1866

Jacob D. Cox (U)
January 8, 1866-January 13, 1868

Rutherford B. Hayes (R)
January 13, 1868-January 8, 1872

Edward Noyes (R)
January 8, 1872-January 12, 1874

William Allen (D)
January 12, 1874-January 10, 1876

Rutherford B. Hayes (R)
January 10, 1876-March 2, 1877

Thomas L. Young (acting) (R)
March 2, 1877-January 14, 1878

Richard Bishop (D)
January 14, 1878-January 12, 1880

Charles Foster (R)
January 12, 1880-January 14, 1884

George Hoadly (D)
January 14, 1884-January 11, 1886

Joseph Foraker (R)
January 11, 1886-January 13, 1890

James R. Campbell (D)
January 13, 1890-January 11, 1892

William McKinley Jr. (R)
January 11, 1892-January 13, 1896

Asa S. Bushnell (R)
January 13, 1896-January 8, 1900

George K. Nash (R)
January 8, 1900-January 11, 1904

Myron Herrick (R)
January 11, 1904-January 8, 1906

John M. Pattison (D)
January 8, 1906-June 18, 1906

Andrew L. Harris (acting) (R)
June 18, 1906-January 11, 1909

Judson Harmon (D)
January 11, 1909-January 13, 1913

James M. Cox (D) 
January 13, 1913-January 11, 1915

Frank B. Willis (R)
January 11, 1915-January 8, 1917

James M. Cox (D)
January 8, 1917-January 10, 1921

Harry L. Davis (R)
January 10, 1921-January 8, 1923

A. Vic Donahey (D) 
January 8, 1923-January 14, 1929

Myers W. Cooper (R)
January 14, 1929-January 12, 1931

George White (D)
January 12, 1931-January 14, 1935

Martin Davey (D)
January 14, 1935-January 9, 1939

John W. Bricker (R)
January 9, 1939-January 8, 1945

Frank Lausche (D)
January 8, 1945-January 13, 1947

Thomas J. Herbert (R)
January 13, 1947-January 10, 1949

Frank J. Lausche (D)
January 10, 1949-January 3, 1957

John W. Brown (R)
January 3, 1957-January 14, 1957

C. William O'Neill (R) 
January 14, 1957-January 12, 1959

Michael V. DiSalle (D)
January 12, 1959-January 14, 1963

James A. Rhodes (R)
January 14, 1963-January 10, 1971

John J. Gilligan (D)
January 11, 1971-January 13, 1975

James A. Rhodes (R)
January 13, 1975-January 10, 1983

Richard Celeste (D)
January 10, 1983-January 14, 1991

George Voinovich (R)
January 14, 1991-December 31, 1998

Nancy P. Hollister (R)
December 31, 1998-January 11, 1999

Robert A. Taft II (R)
January 11, 1999-January 8, 2007

Ted Strickland (D)
January 8, 2007-January 10, 2011

John R. Kasich (R)
January 10, 2011-Current