They say the 7th inning stretch was originated in 1910 when President William Howard Taft, on a visit to Pittsburgh, went to a baseball game and stood up to stretch in the 7th inning. The crowd thinking the president was about to leave, stood up out of respect to the office.
In Japan the 7th inning stretch is called "Lucky 7" and involves fans singing their teams fight song, accompanied by the release of "jet balloons" into the air, creating a unique spectacle where each team's fans sings their song after the top of the 7th inning, while away teams sing theirs after the bottom of the 6th inning.
I've been to MLB games in America where the fans sing "Take Me Out To The Ballpark", but it's nothing like the "Lucky 7" in Japan.