In 1903 Allgood joined the Fays' Irish National Theatre Society as Princess Buan in The King's Threshold. In 1904 she played Cathleen in Riders to the Sea and late that year made her first appearances in Dublin with the Abbey Theatre Company. During the next 10 years with the Abbey, she also played Mrs. Delane in Hyacinth Halvey and Widow Quin in The Playboy of the Western World. She joined the Liverpool Repertory Company in 1914, later played with other companies at Manchester and Stratford, and appeared in several plays with her younger sister, Maire O'Neill. She toured Australia in 1916 in the title role of Peg O' My Heart and appeared as Mrs. Geogheghan in The White-Headed Boy at the Abbey Theatre in 1920. For the Abbey Players, she created the original Juno Boyle in Juno and the Paycock (1924) and the first Bessie Burgess in The Plough and the Stars (1926). The former role was repeated in New York City in 1940 and became the actress's swan song to the legitimate stage. She settled in the United States and thereafter worked only in motion pictures.

Allgood's film debut took place in the first British talkie, Blackmail (1929), and her other English-made films include The Passing of the Third Floor Back (1935), Storm in a Teacup (1937), and Kathleen (1938). Her American films include How Green was My Valley (1941), Roxie Hart (1942), Between Two Worlds (1944), Jane Eyre (1944), The Lodger (1944), The Spiral Staircase (1946), Mourning Becomes Electra (1947), My Wild Irish Rose (1947), and Cheaper by the Dozen (1950).