I first saw Robert Altman on the Rashomon DVD released by Criterion. In a 15 minute introduction to the movie, Altman explained the movie and the effect Kurosawa had on him. It would have been easy to admire Altman, but after that introduction I began to like him.
Altman died of cancer on Monday in Los Angeles. He was 81. His death is almost a personal loss to me. That may sound arrogant, but I am truly saddened.
Rarely does a director, who was in his prime in the 1970s, make such a comeback as Altman did in the 90s and later with Gosford Park (2001). Rarely does anybody work on a variety of genres, and leave upon each of them his own stamp. This is a good time as any to watch Altman films. I am sure you will like him too. Why don't you start with M*A*S*H, Nashville, The Player and Short Cuts?
But don't end it there. McCabe and Mrs Miller, The Long Goodbye, and Popeye, keep watching.
Read more about Altman and the films he made here.
UPDATE: Here's A.O. Scott with the entire list of movies Altman made.