Davis first became popular in daytime television playing opposite Beverlee McKinsey as her character Iris Cory's former (and presumed dead) husband, Elliot Carrington, on the soap opera Texas, a spin-off of Another World, from October 1980 to December 1981.

Davis played his most famous character, Niles the Butler, on the television series The Nanny throughout its run from 1993 to 1999 and in its reunion special in 2004 (in cameo flashbacks only).

He also used an English accent as Professor Moriarty in the Star Trek: The Next Generation episodes "Elementary, Dear Data" and "Ship in a Bottle".

However, as the commanding officer of the aircraft carrier USS Enterprise in the 1990 film The Hunt for Red October, Davis spoke with his own American accent.

Off-Broadway, he played Rubin in Lake No Bottom in 1990, the Duke of Buckingham in The Tragedy of Richard III, and he starred as Gaev in The Cherry Orchard in 2011.

[8] In 2000, Davis was nominated for a Best Featured Actor Tony Award for his role in David Hirson's Broadway play Wrong Mountain.

In November 2010, Davis was part of the Celebrity Autobiography series at the Long Center for the Performing Arts in Austin, Texas.

[12] In 2015, Davis starred in a one-off performance in A. R. Gurney's Love Letters opposite Lauren Lane with proceeds going to the Texas State BFA Acting Program.