THEY MAY don’t have the cachet of the Pulitzer or Booker, but the Sidewise Awards for Alternate History deserve respect. The genre of hypothetical fiction is growing rapidly, with works of surprising quality and originality. Take Sidewise’s latest long-playing winner, Francis Spufford’s “Cahokia Jazz.” A noir thriller set in the 1920s, it imagines an America in which the indigenous population was not nearly wiped out by smallpox. Other winners of the 29-year-old prize included Laurent Binet’s “Civilizations,” which imagines that the Incas invaded Europe in 1531, 39 years after Christopher Columbus discovered the Americas. Changing history is surely as much fun as a novelist can have: losers become winners, and everything doesn’t really change. What if General Lee had won at Gettysburg? What if Napoleon had escorted Wellington and Blücher to Waterloo? Nazis are over-represented on the alternative history bookshelves as in other sections of most libraries. “The Plot Against America» by Philip Roth, for example, placed Charles Lindbergh, an alleged Nazi sympathizer, in the White House. Not far behind is John F. Kennedy, who skipped that visit to Dallas, or perhaps fell victim to the Mafia/Cubans/Russians/Lyndon Johnson. As this selection of the best alternative history novels demonstrates, the world of imagined pasts is rich and potentially infinite.