Manassas, Again by Gregory Benford. A boy is caught up in a war between humans and rebel mechs (robots) against a very different historical background.
Dance Band on the Titanic by Jack L. Chalker. A sailor gets a job on a very mysterious ferry, which travels to places not found on maps and contains a remarkable variety of people, many of whom seem not to recognise each other's presence.
Bring the Jubilee by Ward More. I read this long story a couple of years ago and reviewed it on this blog in January 2012, so I didn't read it again.
Eutopia by Poul Anderson. This is the other story in this collection that I had previously read, but so long ago that I didn't remember much about it (except for the punchline, unfortunately!). The key is a different world in which Alexander the Great had lived to an old age, establishing a Hellenic Empire which survived to the present day, developing advanced science including the ability to travel between alternative worlds. A Hellene exploring one of these worlds flees the wrath of a local ruler in an alternative America, having unwittingly broken a local taboo.
The Undiscovered by William Sanders. Told from the viewpoint of a native American at the time of the first European settlements, this world differs from history in that William Shakespeare is accidently transported to America and is captured by the natives, who he tries to impress by writing a play for them. Carefully researched, and simultaneously funny and sad.
Mozart in Mirrorshades by Bruce Sterling and Lewis Shiner. A nightmare scenario in which travellers to alternate worlds are only interested in pillaging anything of value and couldn't care less about their impact on the locals. One such visit is to Vienna when Mozart is a lad, with unexpected consequences.
The Death of Captain Future by Allen Steele. A spaceship crewman down on his luck is forced to work with a captain lost in a fantasy that he is the Captain Future of old comic-book fame, but the situation changes when they investigate a distress call. Not obviously an alternative history story.
Moon of Ice by Brad Linaweaver. A story that starts with the state funeral of Hitler in 1965 is obviously in the "Nazis won World War 2" camp, in this case by being the first to develop the atomic bomb. What happens next is seen through the eyes of Joseph Goebbels as he becomes caught up with the very different agendas of his rebellious daughter and fanatical son.
Taking both parts of my review together, this is a difficult group to pick favourites from. If I was giving out an award for story quality it would go to Kim Stanley Robinson's tale, which I think would appeal just as much to non-SF fans. Niven's brief story is perfectly crafted and Poul Anderson is a great story-teller, while Chalker's mysterious scenario has a strong appeal to me. They are all worth reading, however.