Here are an unusal lot, directors who remade their own films later in their careers. Comedy directing legend Leo McCarey remade his own 1939 film 'Love Affair' (itself nominated for 6 Academy Awards) as the 1957 movie 'An Affair to Remember' starring Cary Grant. The remake, which used the same screenplay, is now even better regarded than the original:
Alfred Hitchcock remade one of his British sound films, 'The Man Who Knew Too Much' (1934), during his Hollywood years n 1956, with James Stewart and Doris Day starring (though the original didn't have a bad cast either - Peter Lorre!). Hitchcock felt that his earlier film was the work of a gifted amateur and his remake the work of a professional director. You can watch the original in full here:
Frank Capra remade his acclaimed 1933 film 'Lady for a Day' (which was nominated for Best Picture and Best Director at the Oscars) as the 1961 film 'Pocketful of Miracles'. Ok, so this time the results were not so great, largely due to the fact Capra chose to adapt Robert Riskind's original script and, his last film, it was also the work of a director whose powers had sadly diminished. But regardless, it is still a fun film (apparently Jackie Chan's favourite ever - he remade it in Chinese in 1989 as 'Miracles'):
There is not an embed code, but you can watch a clip for the original here and the trailer for the remake here.
Capra, Hitchcock and McCarey's remakes all share something in common: an old black and white film had been turned into a colour film. In Capra's case, it was his first (and only) film in colour. When the Japanese director Yasujiro Ozu turned to colour filmmaking at the end of his career, he also turned to remakes. But in his case they were not just to add colour to his older work, but also sound. In 1959 Ozu remade both his 1932 silent 'I Was Born, But...' and his 1934 film 'A Story of Floating Weeds' as 'Good Morning' and 'Floating Weeds' respectively.
Anyway, an eclectic mix. Let me know if you can think of any other cases of this happening. These are just the ones I knew of. There must be loads.