Stage
Cassidy played Frederic in the 1981 national tour of Gilbert and Sullivan's The Pirates of Penzance before taking over the role on Broadway in 1982. Cassidy's next Broadway role was Jeff Barry in the Ellie Greenwich jukebox musical Leader of the Pack, which opened in April 1985. He originated the role of The Balladeer in the original Off-Broadway production of Stephen Sondheim's Assassins at Playwrights Horizons, which opened in December 1990 in previews.
Cassidy starred at the Elitch Theatre's production of The Robber Bridegroom in 1991. This was the 100th anniversary of the theatre and it was the final production there before it was dormant for over 20 years.
In 1993, Cassidy starred as Bobby opposite Carol Burnett in a Los Angeles production of Sondheim's musical Company. In 1995, he portrayed John Wilkes Booth in the Los Angeles Repertory staging of Assassins.
In 1998, Cassidy played Macheath in a Los Angeles Reprise! production of The Threepenny Opera; he was nominated for the Garland Award for Best Actor for his work in the role. In 1999, he played the title character Joseph in a national tour of Joseph and the Amazing Technicolor Dreamcoat.
In 2000, Cassidy co-starred with Cheryl Ladd in Annie Get Your Gun on Broadway when he took over for Tom Wopat in the role of Frank Butler. He later reprised his role of Frank Butler alongside Patti LuPone and George Hearn in August 2010 concert presentations at the Ravinia Festival in Illinois, directed by Lonny Price.
In 2001, Cassidy played Radames in the national tour of the musical Aida; he won the 2002 National Broadway Theatre Award for Best Actor in a Touring Musical before playing the role on Broadway in June 2002.
From 2004 to 2005, Cassidy was back on Broadway in 42nd Street when he took over for Patrick Ryan Sullivan as Julian Marsh playing opposite his mother as Dorothy Brock. He appeared in a US national tour of Joseph and the Amazing Technicolor Dreamcoat, once again playing the title role, starting in September 2005.