The Newhouses: Si still heads Advance Publications, which was founded by Samuel Newhouse in 1922. Conde Nast is by far the most prestigious property of Advance. Si is known to be mercurial, and doesn't always give warning before making major moves. If he ever does reach his breaking point with Conde's decline, his resulting decisions could be characteristically large, and sudden.
The Grahams: Katherine's father Eugene Meyer bought the Washington Post in 1933. Katherine married Phillip Graham, who led the Post until his suicide in 1963. She took over, and was legendary. Now her son Donald runs the place. With their connections to Warren Buffett, and a company that's diversified well, they may be the best positioned family of the bunch to ride out the bad times and keep going.
The Chandlers: They ran the LA Times from the early 20th century up until Sam Zell bought Tribune in 2007. They got out just in time, apparently.
The Sulzbergers: Arthur Hays took over as publisher of the New York Times in 1935; his son Punch took over in 1963, and his son Pinch, the current mastermind, took over in 1992. The Sulzberger family controls the company through a dual-class stock structure that ensures they can't be taken over without their assent. But they had to cut their precious dividends recently, and the younger Sulzbergers may not feel the strong attachment to the paper that their forefathers did—who had it in richer times. This could very well be the final generation of their leadership.
The Bancrofts: The Bancroft family got the Wall Street Journal passed on to them by Clarence Barron just before the Great Depression, and controlled it Genteel-ly for the next eight decades. Rupert Murdoch bought them out in 2007 with an overly generous offer. They were criticized at the time for being sellouts—which they clearly are—but now they look wise, financially at least. Don't expect to see them come roaring back as media barons.
As you can see, unless the Murdoch family and others step their genteel games up, this sort of thing will go right out of style.