This is Eastwoods fourth directing nomination; he has ten in total; he previously won for directing Million Dollar Baby and Unforgiven.
Clint Eastwood [imdb] Letters from Iwo Jima [imdb]
Stephen Frears for The Queen
This is Frears second Oscar nomination; he has never won.
Stephen Frears [imdb] The Queen [imdb]
Alejandro Gonzalez Iñárritu for Babel
This is Inarritu’s first directing nomination; he is also nominated for producing Babel
Alejandro Gonzalez Iñárritu [imdb] Babel [imdb]
Paul Greengrass for United 93
This is Greengrass’ first Oscar nomination.
Paul Greengrass [imdb] United 93 [imdb]
Martin Scorsese for The Departed
This is Scorsese’s sixth Oscar nomination for directing; he is the favorite to win.
And if he doesn’t, most likely a mob of angry people a la Frankenstein will swarm the Shrine Auditorium and attack Academy voters.
@Cinefille 
I know Scorsese will win, but I really like Stephen Frears. As far as the others, Innaritu seems like too much of a novice, Eastwood has enough already, and Greengrass is just a bit weird for my taste. I wasn’t very impressed with “United 93”.
Innaritu isn’t a novice at all. His earlier movies are just better than “Babel”.
Greengrass is nominated because “United 93” shows the chaos and heroism of 9/11 without the overblown dramatics. It is really a great movie.
I like Stephen Frears as well, but the Oscar pretty much has Scorsese’s name written on it.