i realize that this is a topic that has been done before, but i've already done these types of posts for tommy davis, bob miller, and mike morgan, so i would feel remiss to leave out the most well-traveled player of all-time, octavio dotel. especially since he was, for a short time like the others mentioned, a dodger.
dotel's big league career began with the mets (that's one team) in 1999 (here's a 2000 upper deck card)
even winning a game in the nlcs against the braves that year. however, dotel was traded to the astros (two) in december of 1999 in the mike hampton deal, so he got an astros card in the later series of that same set
the astros converted dotel to a reliever, and he pitched for them for four-plus seasons before he was sent to the a's (three) during the 2004 campaign in the three-team deal that netted the 'stros carlos beltran. this is a 2005 fleer tradition card
after finishing out the 2007 season with the braves, dotel spent 2008 and 2009 with the white sox (seven) before joining the pirates (eight) for the start of the 2010 season. at the trading deadline that year, the dodgers (nine) sent james mcdonald and andrew lambo to pittsburgh for dotel. topps was kind enough to fake him into a dodger uniform for the 2010 update set (here's the walmart black parallel)
dotel began the 2011 season with the toronto blue jays (eleven). here's his 2011 topps card
he was back in the world series again in 2012, but this time it was as a member of the detroit tigers (his thirteenth team - a major league record). here's his 2012 topps update card showing him as a motor city kitty
13 teams in 15 seasons is pretty impressive, and i'm glad dotel came through los angeles on his tour of duties, even if ned gave away mcdonald and lambo for six weeks of a replacement level reliever.