I'll start with his role as Tom Hagan as The Godfather and The Godfather Part II. He was one of many actors in those films that had a great screen presence, when he refused to reprise his role in Part III it made the film less enjoyable. I was watching this documentry on Marlon Brando, where a bunch of actors who have worked with him both on stage and film were talking about him, and on the set of The Godfather, he, James Caan, John Cazale, and Al Pacino were finally about to meet their idol Marlon Brando, after the producers finally yield to Coppola who was battling to get Brando in this film (he also wanted Laurence Olivier who was too ill at the time). So Robert decides they should break the ice with Marlon. I don't exactly remember how it all went, but I think that they went to go pick up Marlon with two cars, Robert and I think Al were riding with Marlon, with Jimmy and Freddie riding in the other. Before they got in, Robert says to Freddie that he should moon Marlon Brando when his car pulls up to him, and the only person who wasn't in on this was Pacino, who admits he had no sense of humor. So they are in their cars (I think this was on set in the cars featured in the film) and Jimmy pulls down his trousers and sticks his ass out the car window for Marlon to see. And Robert who was telling the story did a great impression of Marlon laughing, saying he was obviously amused by the thing and was making remarks about Jimmy's behind. I haven't heard this story anywhere else, but if you can find it and see for yourself how Robert tells it.
Oh I will always remember him for his scenes with the movie producer. The horse head in the bed.
One of my all-time favorites, but his best role bar-none was Gus McCrae in Lonesome Dove.