The seventh-inning stretch has been a longstanding tradition in baseball that is believed to have begun in New York as far back as 1882. However, standing up to stretch our legs, arms and backs during the middle of the seventh inning really didn't become a widespread tradition until April 14th, 1910.
President William Howard Taft attended the opening game between the Washington Senators and the Philadelphia Athletics. During the middle of the seventh, President Taft stood up to stretch because he was sore from sitting for so long. When he rose to his feet, the rest of the crowd felt obligated to do the same, and since then, it's been a tradition in every ballpark.