Stalin executed his political enemies during The Great Purge, which is allegorically depicted when Napoleon holds public executions. Both Stalin and Napoleon tyrannize over their subjects and rule as omnipotent autocrats.

In George Orwell's Animal Farm, the pig Napoleon was based on the U.S.S.R.'s brutal leader, Joseph Stalin. Both Stalin and Napoleon were power hungry and put power above everything else. Napoleon trained the farm's dogs in order to exterminate anyone who might go against him. The dogs were representative of Joseph Stalin's secret police--the KGB. Stalin was also a propaganda "king," who used all types of propaganda to control the people. Napoleon's henchman, Squealer, fulfilled this purpose in Animal Farm. Stalin had a five year plan for the purpose of getting agriculture and industry back up and running, and this plan was what the windmill on the farm symbolized. Furthermore, Stalin exiled Leon Trotsky, much like Snowball was chased off the farm by Napoleon and his dogs. 

Napoleon, the autocratic leader of Animal Farm, eventually changes the name of the farm back to Manor Farm.  Stalin, on the other hand, maintained the name of the socialist republic.  Stalin continued to support communist uprisings in Europe and Asia during the early Cold War, while Napoleon did not send out the pigeons who were supposed to carry revolution to other farms.  Napoleon claimed that the revolution was finished, while Stalin continued to keep the idea that there were always impure elements in the state and society that should be purged.  Napoleon, while he did not encourage the view of Sugar Candy Mountain (Animal Farm's heaven), did give Moses the Raven food.  Stalin, on the other hand, persecuted people of all faiths and claimed that the Soviet Union was an atheist republic.  Stalin purged his own generals in 1937-1938 while Napoleon only saw Snowball as his chief rival and he even seemed to cultivate the other male pigs as followers, provided that they knew they were below him.  While both leaders conducted mock trials and public executions, Stalin killed far more people and even persecuted certain ethnic groups such as Chechens, Tatars, and Ukrainians whom he viewed as a threat.  

I would say that another similarity between both Stalin and the world depicted in Orwell's work is evident through the use and control of information.  The Stalinist control of the flow of information through Pravda and Squealer's masterful presentation of information are both powerful reminders of the level to which the government sought to increase and validate its control over the people.  The idea of "truth" being both the instrument of propaganda for both the Stalinist government and Squealer acquires even more relevance in that both represent the concept of "truth" as being something directly controlled by the government.  At both of their heights, Squealer and Pravda refused to acknowledge anything other than the monolithic supremacy of their ruling authorities, seeking to rewrite both present and past, and ensuring that generations understood state controlled mediums of information as the "only game in town."

There are tons of similarities between this book and various episodes in Stalin's long reign.  Let me highlight a few of them:

• The poor harvests and hard times in the book are true to life.  Stalin's efforts to force Soviet farmers onto collective farms led to a huge famine that caused many deaths in the country.
• The purges of people for crimes that were probably imaginary are also true to life.  When all the animals are executed for conspiring with Snowball, it is very much like the show trials that Stalin put on for people who allegedly opposed the revolution.
• Stalin's inability to really see through Hitler's intentions is portrayed in how Frederick fools Napoleon.  Hitler and Stalin had a nonagression pact that lasted up until the day that Germany invaded the USSR.

Joseph Stalin was a complex personality who led the Soviet Union for almost thirty years. Napoleon is a fairly simple character in a brief allegorical text. Moreover, Napoleon's name shows that he is a generalized figure of dictatorship, as well as being a specific caricature of Stalin.

Napoleon is introduced as being a forceful yet one-dimensional personality, "not much of a talker, but with a reputation for getting his own way." He is not initially a leading figure in the revolution, as he is eclipsed by the more intelligent and charismatic Snowball. Stalin, however, was an excellent student, with a talent for drama and poetry, as well as being a revolutionary from his earliest years. Unlike Napoleon, who is initially a mere follower, he showed his intellectual independence at the Tbilisi Spiritual Seminary in the 1890s, long before the fall of the tsar.

While Squealer fulfills the role of Pravda in Animal Farm, creating a web of propaganda around the unimaginative Napoleon, Stalin wrote the propaganda in Pravda that helped to propel him to the leadership of the Party. His intellectual and ideological commitments contrast with Napoleon's simple quest for power. Despite his brutality and tyranny, Stalin never betrayed the revolution in the transparent way that Napoleon did. Napoleon's actions in selling Boxer for commercial gain and renaming "Animal Farm" as "Manor Farm" suggest a capitulation to capitalism which was not in Stalin's nature.