1912
He ran against Taft in 1912.
It happened in 1912, when Roosevelt went up against Taft.
Richard Nixon, the then Vice President won the Republican nomination.
Gramm made a bid for the Republican presidential nomination in 1996.
James G. Blaine. Senator from Maine, was the Republican nominee for president in 1884, but lost to Cleveland. Edmund Muskie, vice-presidential candidate in 1968, was the front-runner for the Democratic nomination in 1972 but lost the nomination.
Ulysses S. Grant won the U.S. Presidential Elections of 1868 and 1872. He tried but failed to win the Republican Party Presidential Nomination in 1880.
Jesse Jackson, Sr. was the first person of African descent to campaign for a major-party presidential nomination, in 1984 (the Democratic Party). Jesse Jackson competed for the Democratic Party Presidential Nomination again in 1988. Alan Keyes campaigned for the Republican Party Presidential Nomination in 1996, 2000 and 2008. Herman Cain campaigned for the Republican Party Presidential Nomination in 2000 and 2012. Al Sharpton and Carol Moseley Braun campaigned for the Democratic Party Presidential Nomination in 2004. On August 27, 2008, Barack Obama officially became the first person of African descent to receive a major-party U.S. Presidential Nomination.
Margaret Madeline Chase Smith was an unsuccessful candidate for the Republican nomination in the 1964 presidential election, but was the first woman to be placed in nomination for the presidency at a major party's convention.
In mid-2012, Romney is seeking the nomination by the Republican party as its Presidential candidate in the November, 2012 election (likely running against incumbent president Barack Obama).
Did Fredrick Douglass become Vice President
In the Wikipedia article about the election, there is no mention of any other Republicans running for President. At the Republican convention, Grant was elected unanimously on the first ballot.