Born in Oakland, California, Plummer attended Anderson Union High School in Anderson, California. He was signed by the St. Louis Cardinals on April 25, 1965 as an amateur free agent. He played three years in the Cardinals' minor league system, then was drafted by the Cubs on November 28, 1967 in the Rule 5 Draft.

Plummer spent nearly all of 1968 in the minors, making his major league debut at age 21 on April 19, 1968 with the Cubs in a 9-2 road loss to the Cardinals. Pinch-hitting for Chuck Hartenstein, he struck out against Hal Gilson. He had only one more at-bat that season and played in just two games.

He played in the minors for all of the 1969 season. He was traded to the Reds on January 9, 1969 and again played most of the season in the minors, although he was called up to the Reds long enough to play in four games with nine plate appearances, including his first career hit.

While never a regular starter—he was Johnny Bench's backup catcher during the Big Red Machine years—he did play solid defense with a .983 fielding percentage. He was a lifetime .188 hitter. His most memorable game was in 1974 when he hit two home runs off Baseball Hall of Fame member Steve Carlton.

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