Ten directors who have won the Best Director award at the Cannes Film Festival but have never been nominated for an Academy Award:
- Emir Kusturica (Time of the Gypsies, 1989)
- Werner Herzog (Fitzcarraldo, 1982)
- Fernando E. Solanas (Sur, 1988)
- Kar Wai Wong (Happy Together, 1997)
- Bertrand Tavernier (A Sunday in the Country, 1984)
- Pavel Lungin (Taxi Blues, 1990)
- André Téchiné (Rendez-vous, 1985)
- Nanni Moretti (Caro Diario, 1994)
- Mathieu Kassovitz (Hate, 1995)
- Edward Yang (Yi Yi, 2000)
I haven't done an exhaustive examination of the records, but as far as I can tell no one who has ever won a Best Director award at Cannes has won a Best Director Oscar. Of course, Best Director is a fairly minor award at Cannes, since the Palme D'Or goes to the director, but still you'd think there would be some overlap.
mrghoul wanted to see Werner Herzog mentioned in a list. Incidentally, the film mentioned above is the only Herzog film I've ever seen.