The choice of books reflects nothing but my whim on one particular day.
Avram Davidson's The Enquiries of Doctor Eszterhazy, or that's the title on my yellowed paperback edition. After many years out of print, it seems to be back in print under the name of The Adventures of Doctor Eszterhazy, with one additional story. (There are some other Eszterhazy stories that aren't in the collection, alas.) It's set in the Triune Monarchy of Scythia-Pannonia-Transbalkania, and ends just before WWI, with the good Doctor speculating that in times to come the very existence of the Triune Monarchy will be forgotten... a most moving piece for any creator of alternate worlds.
(Most of Davidson's work seems to be out of print at the moment as well, but much of it is excellent offbeat sf, fantasy, or uchronia. I particularly cherish the remark (but from which story, I forget), "I ain't no fooking heretic!")
L. Sprague de Camp's Lest Darkness Fall is an enduring classic of the genre; indeed, Harry Turtledove, the field's best-known practitioner today, was inspired to become a professor of Byzantine history just to find out what de Camp was making up and what he wasn't.... Sprague also wrote "The Wheels of If", a novella that has been available in one form or another (check your local used or sf bookstore), which is about traveling to (or through) uchronias, the main one of which involves a basically Norse America, with interesting conlangish reflections on the development of English (courts without Latin, "Wife" as the title for married women, police are "knights").
Robert Sobel's For the Want of a Nail is that most unusual thing, a straight (non-novelistic) alternative history textbook. The American Revolution is lost after Saratoga goes wrong, and two countries eventually form and struggle for control of the continent: the Confederacy of North America in the East and the United States of Mexico (which has a lot of historical influence from the defeated revolutionists) in the West. The book even includes an afterword by a USM historian which purports to correct the biases introduced by the author, Robert Sobell of the CNA!
A Short History of the Future by W. Warren Wagar is another alternate history book, this time set in the future instead of the past. I found this hard going at first, set it aside, and took it up later and found it excellent. It is more narrative and less documentary than the Sobel book, and the sound of axes being ground is frequently audible, but still worth reading.
What If? ed. Robert Cowley is written by a bunch of historians, and is like Sobel's work, except not consistent; each author writes either an essay or a brief note on a turning point and how it turned out differently. Fascinating insights on odd little bits of history.
Not uchronian, but with a similar offbeat slant, is Barbara Tuchman's The First Salute, which is a history of the American Revolution from the Dutch viewpoint. (Tuchman got me interested in history with her brilliant narratives: anything by her...I probably shouldn't say that; Stilwell and the American Experience in China was too long and over-detailed.)
The Man in the High Castle by Philip K. Dick is a classic uchronia about a defeated United States partitioned between Germany and Japan. Many consider this Dick's best work, although I am sneakingly fond of Clans of the Alphane Moon, about a small planet settled exclusively by the insane.
The Two Georges, by Turtledove and Richard Dreyfuss (the actor), is a mystery about the theft of the eponymous painting, depicting the reconciliation of George III and George Washington, set in an Imperial North America, complete with airships and a Franco-Spanish enemy (plus the usual where-are-they-now moves: John F. Kennedy publishes a revolutionary newspaper, Richard Nixon really is a used-car salesman, Sir Martin Luther King is the N.A. viceroy...). The scenes in the Six Nations (Iroquoia) are especially interesting.
Orson Scott Card's Alvin series (Seventh Son, Red Prophet, Prentice Alvin, Alvin Journeyman, Heartfire) are another American uchronia set in the first two decades of the 19th century. The premise here is that "folk magic" actually works: people have "knacks" that allow them to do more or less supernatural things. In addition, England and New England are ruled by the Cromwellian Protectorate (but way less tolerant than Cromwell's actual regime), the Southern colonies are controlled by the King in Exile (currently Arthur Stuart), and the United States (reduced to New York, New Jersey, and Pennsylvania, though divided into more parts), maintains a cautious neutrality between them. If you can swallow the fantasy elements and have no trouble with the (rather mild) backwoods dialect in which the books are written, I can recommend these.
Harry Harrison is one of the most uneven writers I know: the Stainless Steel Rat series is funny but lightweight; A Transatlantic Tunnel, Hurrah! is unreadable bilge; the Deathworld trilogy is excellent classic sf (notable for the use of a degenerate Esperanto; H.H. is an Esperantist); and The Daleth Effect (thanks, Dave Empey), which is about a Jew who discovers the ultimate bomb and promptly flees to Denmark, the only country he thinks he can trust not to misuse it), is extremely moving, especially for its avoidance of a facile happy ending.
Anyway, Harrison's Hammer & Cross uchronian series (The Hammer and the Cross, The One King's Way, King and Emperor) is rather too sanguinary for my usual taste, but I found the reformed paganism (the Way) extremely interesting from a concultural viewpoint; the books are about the creation of a unified Scandinavian/English empire in the 9th century.
Alternate Presidents, ed. Mike Resnick, is an excellent anthology of stories about uchronian U.S. presidents. They are printed in chronological order, but one must keep firmly in mind that each story does not presume its predecessors, but rather presumes actual history. (In a few cases, the story is set after, rather than during, the actual point of departure). The letters from Queen Victoria to President Victoria Woodhull (1872) are priceless, particularly when read aloud in your best Lady Bracknell impression.