In 1992 Palmer became the first Texas ballplayer to ever homer in the first three games of a season, a feat that was matched in 2011 by Ian Kinsler and Nelson Cruz.
He was elected to the American League All-Star team in 1998, and he led the league in strikeouts in 1992 with 154. Palmer was the recipient of the Silver Slugger at third base in 1998 with the Kansas City Royals and 1999 for the Detroit Tigers.
Palmer retired following the 2003 baseball season, after various injuries limited him to fewer than 100 games over the three previous seasons. He attempted a comeback with the Tigers during 2005 spring training, but failed to make the team, after which he retired again.