If we’re going to start throwing around dead writers - a much more pleasant sport than the image would suggest - then I have to mention P. G. Wodehouse.
He lived from 1881-1975 and published books right down to the end. Well past the end, actually, as three novels, three short story collections and a few miscellaneous other books were published posthumously. It can be argued that his style never changed much in all those years either.
If you want to count playwrights, I saw a new play by Arthur Miller (born in 1915 according to imdb) last year, and a new Edward Albee production (born in 1928, so a little young for the list) the year before that.
Now that’s a P.G.-rated simulpost.
George MacDonald Fraser, author of the **Flashman ** series, is well into his eighties and still going strong: Flashman On The March is due out in, well, March, and I’m going to be sleeping outside the bookstore.
I tell a lie - I assumed because he was a WW2 veteran he was older, but he was born in 1925 or 1926, depending on which sites you believe: he can only have been 19 or 20 when he served in Burma. Never mind, that just means more Flashmans.
Studs Terkel is 92 and his last book was published in 2001. As far as I know, he is still active.
Although she didn’t write much, Queen Victoria lived so long that we still talk about the Age of Victoria.
As I mentioned in the same thread, Evan Hunter (who also writes as Ed McBain) is still going strong at 78, still writing and publishing, and as he e-mailed to me “I plan to die at age 90 while writing a 87 Precient mystery.” The sheer volume of his works is staggering, and they are also very, very good. He has written an 87 Precient novel called “EXIT,” which will be published after he dies, and will be his last.
I honesty think he will break Wodehouse’s record.
At the other end of things Norman Maclean didn’t write his first work. the brilliant, A River Runs Through It until he was in his 70s.
George Seldes died at age 104, while working on a revised edition of his book The Great Thoughts.
Henry Roth may have had the longest writer’s block ever, with a 59 and a half year gap between his first novel and his second.
Jule Styne’s last musical premiered when he was 88.
I wish I could remember the guy’s name now for this thread but I read an article in the Irish Times a while ago that featured a writer who had just published his first novel at the age of 84 or something. I was impressed. Don’t know if it was a great novel but still. Gives hope to all of us who say ‘I must write that novel some day’ 
There have been many great writers who did not get serious until middle age or later. (One of the best novels ever written about the south, for example, was Olive Ann Burn’s Cold Sassy Tree, which was not even begun until the author was in her mid fifties.)