The Giants with 20.
Don Mattingly hit a home run in ten consecutive games for the Yankees in July of 1987. Rocky Colavito hit four home runs during four consecutive at-bats in one game when playing for Cleveland in 1959.
If your talking one player then five but in college baseball Fresno state hit back to back to back to back to back to back jacks
Hank Aaron 755
Marshall Mcdougal hit 6 home runs in 6 at bats in 1 game for Florida State Universtiy Dale Long and Don Mattingly each hit home runs in eight consecutive games. No major league has hit homers in 6 consecutive at bats. Four has been done a few times.
Barry Bonds set the single season home run record with 73 home runs in 2001.