I was aimlessly searching players on Baseball Reference and watching a game when the announcers mentioned Kevin Mitchell. This prompted me to look up Keith Mitchell. I was amused to find he played parts of four seasons in the majors, on four different teams, and never in two consecutive seasons ('91 Atlanta, '94 Seattle, '96 Cincinnati, '98 Boston.) His prolific career spanned all of 128 games.
So, for anyone with a better knowledge of baseball stat-finding than me: Has anyone ever played fewer games for more teams in a major league career?