Mays appeared on Broadway in I Am My Own Wife, a Pulitzer Prize-winning play by Doug Wright, from November 2003 (previews) to October 31, 2004. He had appeared in the play Off-Broadway at Playwrights Horizons in May 2003, and at the La Jolla Playhouse in July 2001. Mays won the 2004 Tony Award for Best Performance by a Leading Actor in a Play, the 2004 Drama Desk Award for Outstanding One-Person Show, an Obie Award, and a 2004 Theatre World Award for his solo performance. He also won the 2007 Helpmann Award for Best Male Actor in a Play for seasons of I Am My Own Wife in Australia in 2006.