You can't tell the players without a scorecard. Long ago, vendors yelled that in order to sell scorecards, but today, nothing could be closer to the truth. Today's players change teams more often than Hillary Clinton, Barack Obama, and John McCain change political positions, but at least nine players have played on four teams during the same season.
Once upon a time, more than a century ago, there was a player named Frank Huelsman. In 1904, Frank Huelsman changed teams four times. Huelsman played for St. Louis in 1897, appearing in only two games and hitting .286. He was a career minor leaguer who played over twenty years, batting .342, winning five batting titles and leading his league in RBIs six times. In 1901, the American League was formed, creating a need for players. In 1904, Huelsman joined the White Sox but it was only for a brief stay. On May 4, the 6'2" outfielder was sold to the Tigers, where he played only 4 games before the Tigers sold his services to the Browns. It wasn't over. On July 14, the Browns traded Huelsman to the Senators, where he played the rest of the season. His overall batting average was .245, but he played on four teams.
Frank Heulsman isn't the only player to have been with four teams in a single season. Nine players, including Heulsman, have had the experience. In 2000, Dave Martinez, started the season with Tampa Bay, went to the Cubs, then to the Rangers, and finally ended the season as a loyal member of the Blue Jays. In sixteen seasons, Martinez played for nine different teams, batted .276, and despite being with so many teams, he didn't get to the playoffs until his final season of 2001 with the Braves.
Dave Kingman hit 442 home runs but wore out his welcome with almost every team he played for. Originally drafted in June,1967 by the Angels, Kingman didn't sign. In January, 1968, he was drafted by the Orioles and didn't sign. Finally, he was drafted by the Giants in 1970 and signed. He remained with the Giants until the Mets acquired his services in 1975, and then, on June 15, 1977, the Mets traded TomSeaver to the Reds because Seaver wanted too much money. They also traded Dave Kingman to the Padres for utility player Bobby Valentine. Interesting, isn't it? Anyway, the Padres didn't keep Kingman long. On September 6, the Padres sent Kingman to the Angels, the team referred to by many names, for cash. Nine days later, the Angels sent the slugger to the Yankees for cash. Kingman became the first player to play in all four divisions in a single season (Mets in the NL East, Padres in NL West, Angels in AL West, and Yankees in AL East).
Other players who have been with four teams in a single season include pitcher Willis Hudlin in 1940, outfielder Paul Lehner in 1951, pitcher Ted Gray in 1955, outfielder Wes Covington in 1961, and pitcher Mike Kilkenny in 1972. The "feat" is quite unusual. One might conclude that in the era of free agency, it is more likely to occur than ever before, but there are two factors against it. The first is that most players have huge contracts that makes moving them difficult, while the other factor is that players with low salaries become more desirable and less likely to move.
References:
Frank Huelsman at Baseball Library