A question is circulating on SABR-L, the email list for SABR members, regarding Dave Kingman's improbable 1977 season, in which he played for four separate teams, one per division, including both New York teams. The question was whether anyone else had matched or bettered Kingman in in-season migratory patterns.
There were a bunch of emails mentioning other quad-teamers, but no one had a complete list. Well, it seems that I am fast becoming the Shell Answer Man for odd SABR questions. I ran a nice little nine-table query and voila, got an answer.
First, Kingman was eclipsed by five-teamer Frank Huelsman. In 1904, Huelsman played for the White Sox, the Tigers, the Sox again, the Browns, and the Senators. Technically, that's four teams, but he did have two separate stints with Chicago. I couldn't find any information on why Huelson became such a hot potato. Baseball-Reference only had one transaction from Chicago. One thing to consider is that teams frequently loaned players to other teams in the olden days before farm systems. This was especially true when leagues failed to act in concert regarding player ownership and leagues tried to retain players for themselves. Not that this was the case in 1904—The NL and AL had already come to an agreement in 1903—but it's something to keep in mind.
In total there have been 19 players who had four separate stints with different teams in a season. Many of them, like Huelson, spent more than one stint with the same team.
As for Dave Kingman, he is the only man to have played for all four divisions, but that might be attributable to the era in which he played more than anything else. There were four divisions in the majors from 1969 to 1993, inclusive. Kingman was one of just three men to play for four teams in that era. He just turned out to be the lucky one. Dan Micelli played for four teams in four different divisions in 2003, but by then the majors had expanded to six divisions, a number that even Dave Kingman would be hard pressed to match. In the days before divisional play, one player, George Strief, managed to play in all three major leagues.
Here's the complete list of four-team players with first their batting and then pitching (if any) stats: