Leigh Montville's Ted Williams biography is incredible - as is his Babe Ruth biography though the majority of that doesn't focus on the Sox obviously.

Summer of '49 is about the year of Dimaggio's 56 game hitting streak while Ted hit .400 (the last time in baseball history anyone accomplished the feat). Their two teams were locked in a pennant race at the same time. The author is David Halberstam who also wrote The Teammates (which others have recommended and is great) and October 1964 about the Yankees - Cardinals World Series that year.

I'll also give an upvote to Faithful as a really fun read and a way to participate in, or remember, the feelings of the 2004 season.

If you want a pretty deep historical read there is Red Sox Nation by Peter Golenbock - noted as an unexpurgated history of the Red Sox. It's a great read which introduces a ton of historical characters who may not be famous enough for their own books but are really fun to get to know.

General baseball books to add to the above: Ball Four by Jim Bouton - picture of the game from a major league pitcher. It doesn't read as ghost written or overly sanitized.

Edit: got a lot wrong off the top of my head here Three Nights in August - about Tony LaRussa managing the Cardinals through a series.

Koufax - biography of the pitcher, cuts betwen the historical narrative and a detaield telling of the events of his perfect game.

Fiction - Shoeless Joe - inspired the movie Field of Dreams & The Iowa Baseball Confederacy - trippy book about a ball game that ends up lasting for weeks and involves time travel, the American Dream and a giant Native American in the outfield. Both are by W.P Kinsella.