Logan Forsythe may not have been considered a utility player, but it is hard not to think of him that way.  When he was traded from San Diego before the 2014 season, Forsythe's first year as a Ray saw him play at least one game at Second, Short, Third, First, Left, and DH.  He didn't move around because he was poor defensively, as he never had a negative Defensive bWAR year in Tampa.  It sounds like quite a versatile player!

Randy Winn was a switch-hitting Outfielder who was plucked from the Florida Marlins in the Expansion Draft.  Winn had yet to break into the Major League level, and his debut at Baseball's highest level occurred in Tampa.

With the Tampa Bay Rays for three seasons (2008-10), Matt Garza started 94 Games.  The righthander would win 11 Games in his first year there, but his crowning achievement was in the ALCS, where he won two Games with a 1.38 ERA, an effort that took Tampa to play in their first World Series.

Rocco Baldelli had an excellent rookie season in 2003 when he debuted in the Majors with the Rays.  Finishing third in American League Rookie of the Year voting, the Centerfielder was seventh in Stolen Bases (27) and tenth in Hits (184), and he would bat .289 with 11 Home Runs.  The 2004 season was also good, with him having a career-high in Home Runs (16) and RBIs (74), and he was first among the AL Centerfielders in Assists and Range Factor per Game.  That was sadly the beginning of the end for Baldelli.