This question is one of the most asked every year in Baseball. The problem is there are no foot markers from home plate to the stands, or even past the stands. From one ball park to the next it is always an estimation. If you want a definitive answer, let us say Mickey Mantle at 656 feet April 17th, 1963 at Washington's Griffith Stadium. Unfortunately, the distance of this home run, like most that are hit a long distance, has probably been exaggerated by the excitement of those witnessing a ball hit so far in an actual game. Mantle's home run has become somewhat of a myth because many people say the distance was measured to the point where it stopped rolling. (To prove the point further, some listings have Mantle's shot at 643 feet, and some say he hit two that traveled at least that far.)
Those who saw him play say Josh Gibson of the Negro Leagues hit the farthest ball ever, at a distance of over 900 feet. Of course, that was with no measurement whatsoever and passed on by word of mouth many times because the Negro Leagues often did not keep accurate records of such things. Suffice to say, there is no super human who can hit the ball 40-100 feet farther than everyone else.
Wikipedia lists the farthest verifiable home run as Babe Ruth at 575 feet out of Tiger Stadium. Based on the scientific research that has been done using physics and geometry, most home runs that have been rumored to have traveled farther have been proven to be inaccurate. This includes Mantle's famous shots
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Ernie White He hit 144 home runs in mlb history.
Darrell Evans and Jim Thome
Hank Aaron
The first home run in MLB history was by Ezra Sutton of the Cleveland Forest Citys on May 8, 1871 against the Chicago White Stockings in the National Association. Sutton hit a second home run in the game to be the player to hit the first and second home runs in MLB history.
586, 7th most in MLB history as of June 30, 2009.