Plummer has played most of the great roles in classic repertoire. In 1953, Plummer was the understudy to Tyrone Power in The Dark is Light Enough, in a production by Katharine Cornell in which she also starred. In his biography, Plummer states that Cornell was his 'sponsor.' In 1973, he appeared on Broadway as the swordsman and poet Cyrano de Bergerac in Cyrano, a musical adaptation of Edmond Rostand's 1897 play Cyrano de Bergerac by Anthony Burgess (libretto and lyrics) and Michael J. Lewis (music). For that performance, Plummer won the Tony Award for Best Actor in a Musical and a Drama Desk Award for Outstanding Performance.  In 1971 he appeared at the National Theatre in the play Amphitryon 38, directed by Sir Laurence Olivier.

In 2002, he appeared in a lauded production of King Lear, directed by Jonathan Miller and performed at the Stratford (Canada) Shakespeare Festival. The production came to New York City's Lincoln Center in 2004, where Plummer's performance as Lear garnered him his sixth Tony nomination.

He returned to Broadway in 2007 as Henry Drummond in a revival of Inherit the Wind, winning a Drama Desk Award nomination as well as his seventh Tony nomination.

Plummer returned to the stage at the Stratford Shakespeare Festival in August 2008 in a critically acclaimed performance as Julius Caesar in George Bernard Shaw's "Caesar and Cleopatra" directed by Tony winner Des McAnuff; this production was videotaped and shown in high-definition in Canadian cinemas on January 31, 2009 (with an encore presentation on February 23, 2009) and broadcast on April 4, 2009 on Bravo! in Canada. Plummer once again returned to the Stratford Festival in the summer of 2010 in The Tempest as the lead character, Prospero.