Joe DiMaggio's 56 consecutive game hitting streak in MLB -- is that also the record for consecutive games reaching base safely?

Most Consecutive Games
(Reaching Base Safely) AL Ted Williams Boston 84 07-01-1949
09-27-1949

Virgil Trucks tells a perhaps apocryphal tale about a game between Detroit and the Red Sox in Boston: "Joe Ginsberg was catching and Williams came up and walked on four straight pitches, and Joe's questioning the umpire about it. On the last one, he said, 'Bill'-Bill Summers was the umpire. He said, 'Bill, don't you think that ball was a strike?' And Bill said to Joe, 'Mr. Ginsberg, Mr. Williams will let you know when it is a strike.'"