[3] Dempsey was selected by the Minnesota Twins in the 15th round of the 1967 Major League Baseball draft out of Crespi Carmelite High School.

Dempsey made his major league debut late in the 1969 season for the division winning Twins managed by Billy Martin, however he didn't qualify for the postseason roster.

[1] Dempsey spent a few more seasons shuttling between the Twins and their minor league teams, before being traded to the New York Yankees for Danny Walton on October 31, 1972.

It was the culmination of an unpleasant conversation between the two players on a one-hour flight which was delayed for three hours at Cleveland Hopkins International Airport.

The Yankees had swept a four-game series from the Indians and were still in contention for the American League East title with two games remaining in the regular season.

[6] After three and a half seasons with the Yankees, the Baltimore Orioles acquired Dempsey along with Scott McGregor, Tippy Martinez, Rudy May, and Dave Pagan for Ken Holtzman, Doyle Alexander, Elrod Hendricks, Grant Jackson.

[17] After only one season with the Indians, he became a free agent once again and signed with the Los Angeles Dodgers, where he would be a member of another World Series-winning team in 1988, this time as a backup catcher to Mike Scioscia.

While playing for the Dodgers in 1990, he became involved in a brawl with Phillies' center fielder Lenny Dykstra, who took exception to Dempsey's "buttering up" the home plate umpire.

[17] His sense of humor during his playing career was renowned, and he was famous for his "rain delay theatre" performances, in which he emerged from the dugout in stockinged feet onto the tarpaulin covering the infield during a rain delay and pantomimed hitting an inside-the-park home run, climaxed by his sliding into home plate on his belly on the wet tarp, all to the raucous delight of the soggy fans.

[8] He sometimes did this while wearing a pair of underpants over his uniform, making fun of teammate Jim Palmer's famous advertisements for Jockey brand briefs.

[1] While he was a light-hitting player, Dempsey's lengthy major league career was due in part to his excellent defensive skills, despite the fact that he never won a Gold Glove.