Alexander is best known for his role as George Costanza in the television series Seinfeld (1989–1998), for which he was nominated for seven consecutive Primetime Emmy Awards and four Golden Globe Awards. Other well-known roles include Phillip Stuckey in the film Pretty Woman (1990), comic relief gargoyle Hugo in the Disney animated feature The Hunchback of Notre Dame (1996), and the title character in the animated series Duckman (1994–1997).
Alexander has had an active career on stage, appearing in several Broadway musicals including Jerome Robbins' Broadway in 1989, for which he won the Tony Award as Best Leading Actor in a Musical and a Grammy Award for Best Musical Theater Album. He appeared in the Los Angeles production of The Producers and was the Artistic Director of "Reprise! Broadway's Best in Los Angeles", where he has directed several musicals.