Go away for a couple of days and big things happen. The saddest, of course, is the death of Ted Williams.
It's interesting to see how the perception of people change over time. Joe DiMaggio was considered the greatest living player from the late 60's on, even though there was ample evidence that he wasn't. DiMaggio did a very good job of managing his public image. He was a beloved player, and stayed beloved through the rest of his life. Williams, on the other hand, had a poor relationship with the fans and the press during his career, and was not well liked at all. Yet, the people I've come across who have met DiMaggio have nothing good to say about him, and the people who have met Williams have nothing but good to say about him. We'll miss you, Ted.

As to who is the greatest living players, I have to go with Mays. He has one fewer win share than Aaron, and Mays missed time in the military. I give it to Mays on defense. Jayson Stark has thoughts about this here.