The World Set Free by HG Wells;
On The Beach by Nevil Shute;
Ape And Essence by Aldous Huxley;
Fahrenheit 451 and The Martian Chronicles by Ray Bradbury;
Twilight World by Poul Anderson (see here).
In CS Lewis' The Hideous Strength, first published in 1945, World Wars I and II "'...were simply the first two of the sixteen major wars which are scheduled to take place in this century.'"
-Lewis, That Hideous Strength (London, 1955), p. 157.
Robert Heinlein predicted "Mutual Assured Destruction" in "Solution Unsatisfactory" and described free men continuing to fight after a nuclear war in "Free Men."
In Isaac Asimov's future history, a far future radioactive Earth probably resulted from a near future nuclear war - although Asimov revised the history later.
In James Blish's A Case Of Conscience, populations wind up living underground in permanent city-sized nuclear air raid "Shelters," even though nuclear war is avoided.
In Jerry Pournelle's CoDominium future history, the Great Patriotic Wars of 2103 end the CoDominium and are followed by the Exodus of the Fleet so they sound like a delayed World War III.
In SM Stirling's Draka timeline, the three major wars of the twentieth century are not numbered but named - the Great War, the Eurasian War and the Final War.
Harry Turtledove describes Anson MacDonald (Robert Heinlein) fighting on after Stirling's Final War.
In Alan Moore's V For Vendetta, "England prevails" under fascist rule after opting out of a nuclear exchange whereas, in the same author's Watchmen, a faked inter-dimensional invasion prevents a nuclear war.
