Randy has appeared in several of the National Lampoon Vacation movies, was nominated for an Academy Award for his role in The Last Detail (1973), won a Golden Globe for his portrayal of the president in LBJ: the Early Years (1987), and was featured (with Margaret Colin) in two science fiction movies, the unsuccessful Martians Go Home and very successful Independence Day.
His television appearances include a season as an SNL cast member (1985-1986), the role of real-life gunslinger John Wesley Hardin in the mini-series Streets of Laredo, and a starring role in the awkwardly-titled The Brotherhood of Poland, New Hampshire (2003).