The Mammoth Book of Alternate Histories by Ian Watson
Every short story in this wonderfully varied collection has in common some diversion in history, some alternate reality from what we know, resulting in a very different world. In addition to original stories specially commissioned from bestselling writers such as James Morrow, Stephen Baxter, and Ken MacLeod, there are genre classics from Kim Stanley Robinson, Harry Turtledove, and George Zebrowski: over 20 stories in all.