“But if it bee well considered, The praise of Ancient Authors, proceeds not from the reverence of the Dead, but from the competition and mutual envy of the Living.”

The attribution of this widely quoted remark about nuclear war to Khrushchev is disputed in Respectfully Quoted : A Dictionary of Quotations (1989) http://www.bartleby.com/73/1257.html.
In Russia this quote is usually attributed to the translation of Treasure Island by Nikolay Chukovsky: "А те из вас, кто останется в живых, позавидуют мертвым!" ("Those of you who will be still alive will envy the dead", originally: "Them that die'll be the lucky ones"). http://www.chitaem-vmeste.ru/pages/material.php?article=89&
Disputed
No instance of this statement, allegedly in reference to nuclear war, has been found in Khrushchev's writings or documented remarks, as indicated in Respectfully Quoted : A Dictionary of Quotations (1989) http://www.bartleby.com/73/1257.html. Herman Kahn used "the survivors [will] envy the dead" in his 1960 book On Thermonuclear War.

Original: (la) Auctoritas siquidem ex vera ratione processit, ratio vero nequaquam ex auctoritate. Omnis enim auctoritas, quae vera ratione non approbatur, infirma videtur esse. Vera autem ratio, quum virtutibus suis rata atque immutabilis munitur, nullius auctoritatis adstipulatione roborari indigent.

De Divisione Naturae, Bk. 1, ch. 69; translation by I. P. Sheldon-Williams, cited from Peter Dronke (ed.) A History of Twelfth-Century Western Philosophy (Cambridge: CUP, 1988) p. 2.

Quote

Fragment 1.

Fable XLIV http://books.google.com/books?id=8Q9IAAAAMAAJ&q=%22envy+is+a+kind+of+praise%22&pg=PA170#v=onepage, "The Hound and the Huntsman"
Fables (1727)

"What Can I Do About It?"

A variant — "Professor Einstein, the learned scientist, once calculated that if all bees disappeared off the earth, four years later all humans would also have disappeared" — appears in The Irish Beekeeper, v.19-20, 1965-66, p74, citing Abeilles et Fleurs (Bees and Flowers, the house magazine of Union Nationale de l'Apiculture Française) for June 1965. Snopes.com mentions its use in a beekeepers' protest in 1994 in Europe http://www.snopes.com/quotes/einstein/bees.asp suggesting invention and attribution to Einstein for political reasons.
Misattributed

Preface to Titus Andronicus, or the Rape of Lavinia (1686); quoted in The Shakespeare Allusion-Book: A Collection of Allusions to Shakespeare from 1591-1700, vol 2, ed. John Munro (1932).

Source: Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry (1871), Ch. III : The Master, p. 67
Context: Reverence for greatness dies out, and is succeeded by base envy of greatness. Every man is in the way of many, either in the path to popularity or wealth. There is a general feeling of satisfaction when a great statesman is displaced, or a general, who has been for his brief hour the popular idol, is unfortunate and sinks from his high estate. It becomes a misfortune, if not a crime, to be above the popular level.
We should naturally suppose that a nation in distress would take counsel with the wisest of its sons. But, on the contrary, great men seem never so scarce as when they are most needed, and small men never so bold to insist on infesting place, as when mediocrity and incapable pretence and sophomoric greenness, and showy and sprightly incompetency are most dangerous.