Yes. Several times. Among the actors who have played two or more different parts are (in no particular order): David Tennant, Karen Gillan, Peter Purves, Nicholas Courtney, Eve Myles, Patrick Troughton, Jean Marsh & Colin Baker. There are many others. If appearances in Torchwood and The Sarah Jane Adventures were also to be taken into account, there would be even more.
-- Jacqueline Hill played Barbara, a companion of the First Doctor. Hill later played a priestess in the serial "Meglos"
-- Nicholas Courtney played Bret Vyon in "The Daleks' Master Plan"; he later played semi-regular character Brigadier Lethbridge-Stewart.
-- Colin Baker played Gallifreyan guard captain Maxil in "Arc of Infinity"; He later went on to play the Sixth Doctor.
-- Peter Purves played an American tourist in the serial "The Chase"; he later appeared as Steven in the same story, and became a companion to the First Doctor then.
Freema Agyeman and Karen Gillan in the new series played other characters (Martha's Cousin, and a Soothsayer) before going on to play Martha and Amy.