Hard to believe these are the "best" alternate history stories, and one isn't really even alternate history, taking place in the future, which of course negates the term "history."
Contents and my rating (* to *****):
The Lucky Strike - something prevents the Enola Gay from dropping its cargo of atomic bombs on Japan. (** -- Well written, but ultimately not that interesting a twist on history.)
Winterberry - a man lives in isolation for years with only his elderly mother and an "uncle" aware of his presence. (** - the twist is telegraphed many pages before the end which defuses some of the impact.)
Islands In The Sea - Muslim emissaries to a coveted area meet with rival factions. (* - when the story has to start with an explanatory paragraph about what happened to get to this point in time, it's a poor start. Ultimately boring.)
Suppose They Gave A Peace - a family is affected by the Viet Nam war. (* - not much alternate history in play and not that interesting a story.)
All the Myriad Ways - a possible contamination from an alternate reality infects a world plagued by suicides. (**** -- first satisfying story in this collection; well thought out and thought-provoking.)
Through Road No Whither - Victorious Nazi's encounter a force they can't control in 1984. (*** - short and interesting take on a different WWII outcome.)
Manassas, Again - Robots vs. Humans during a "civil war." (*** - nicely told take on the possibility of intelligent machines.)
Dance Band on the Titanic - an unemployed deckhand takes a job on a ferry that runs between Maine and Nova Scotia, sometimes. (***** -- best story in the collection is interesting and has great atmosphere.)
Bring The Jubilee - the South wins the Civil War (***** - one of the best tales in this sub-genre. Long story, a novella really.)
Eutopia - while exploring an alternate/parallel universe, a man breaks a sacred taboo and must flee for his life. (**** - one of those stories that strikes home in the last page, paragraph or sentence. In this case, the last word. Thought-provoking.)
The Undiscovered - a noted Englishman spends the remainder of his life in pre-Colonial America. (**** - nice twist and interesting story.)
Mozart In Mirrorshades - After the discovery of alternate realities and time travel, a company goes back to the 1700's to drill for oil in Germany. (*** - light-hearted tale peopled with famous persons of the time.)
The Death of Captain Future - a vagabond space-worker winds up on the rocket ship of a (probably) insane captain who reckons himself a real Captain Future, based on and old comic book hero. (*** - okay but not an alternate history, more a sci-fi story.)
Moon of Ice - A top WWII Nazi contends with even more radical thinkers shortly after the death of Hitler in 1965. (*** - starts out interestingly, but bogs down at the end.)
Some interesting premises, some good writing. A ghostly ferry makes passages between coexisting "different Earths"; a 20th-century man describes his impact on the Civil War, brought about by time-machine tricks; and Mozart, Thomas Jefferson and Marie Antoinette end up as employees at an oil refinery in this compilation, edited by Harry Turtledove with Martin H. Greenberg.
A fascinating genre of sci-fi.