He has been married to his wife Linda since 1965, with whom he has had two children, Ben and Daisy. In 1995, he was diagnosed with lymphoma, which was successfully treated and remains in remission.
Wright has also enjoyed a stage career and has acted at regional theaters around the United States. He received a Tony nomination in 1998 for Ivanov. Another Broadway appearance of note was in Twelfth Night at Lincoln Center as Sir Andrew. He was in the original production of The Great White Hope at The Arena Stage in Washington, D.C. In 2007 he acted at the JET (Jewish Ensemble Theatre) in Detroit and in the production of "No Man's Land" at the American Repertory Theater. He appeared in The Public Theater's 2010 production of Winters Tale and Merchant of Venice at Shakespeare in the Park.
In January 2000, Wright was arrested for drunken driving in Los Angeles. At the time he was appearing on The Norm Show. He was sentenced to probation. Wright had another DUI arrest in 2003. In 2001 several accusations were made by the National Enquirer. after acquiring alleged homemade sex tapes showing Wright smoking crack cocaine and having sex with a homeless man he had met that evening.
