General Zod

Pocket Universe

Zod was one of the three Kryptonian criminals who took over the Time Trapper's pocket universe after Superboy was killed. When Zod, Quex-Ul and Zaora had decimated the entire population of that Earth, Superman was forced to execute them using kryptonite, a deed that would plague his conscience for years.

False Krypton

In the duplicate Krypton created by Brainiac-13, another fascist counterpart of Zod was defeated by Superman.

Russian Zod

The son of Russian Cosmonauts, the unborn boy who would be codenamed "Zed" was affected when Kal-El's spacecraft and a chunk of Kryptonite

Modern Zod: The Great General of Krypton

Just as the El family is a staple among the Scientist guild of Krypton, the Zod family is a staple of the Millitary.  Generations ago Zod's ancestor and namesake, Admiral Dru-Zod  once led the Military Council, in power before the Kryptonian Science Council came to rule, and Krypton to the head of a large empire that scoured galaxies.  That dynasty ended when Bav Sor-El's Science Council was able to convince the people of Krypton of the immorality of the Empire and oust Har-Zod and his Millitary Council during elections.  The Kryptonian Navy would be dismantled, with the exception of Dru-Zod's ship which would haunt Superman later.  The military was delegated to peace-keeping tasks on Krypton, and the Zod's continued to serve.

Months before the destruction of Krypton, Jor-El convinces his friend, mentor and intellectual peer Non that their planet is indeed doomed.  The word of two of the most respected scholars of Krypton was not enough to sway the Council, whose only action in the matter was to forbid any further talk on the subject.  While Jor-El chose to fight a sisyphean battle to convince the Kryptonian Council, Non spread the word to the people.  Non's actions were considered rebellious, and the council dispatched their most fearsome commander, General Zod, to dispatch of him. Zod though is swayed by Non's words and becomes convinced of the impending destruction of Krypton.  His most trusted lieutenant and loyal lover Ursa also joins his cause.

Zod Rebels

The council quickly reacted to the insurrection by kidnapping Non in his sleep and lobotomizing him.  They then arrest the three defectors and sentenced them to the Phantom Zone at the request of Jor-El.  Jor-El agreed to desist in his attempts to convince the Council in return for a humane punishment to death for his contemporaries.  After the verdict Zod declared that the only way to save Krypton was to overthrow the stubborn Kryptonian Council, and by ruling Krypton in their place.  Their brutal escape attempt was quelled, but not before members of the Council were slaughtered.  The verdict still stood though, as the judgment of the Council is final, and Jor-El administered the punishment, banishing them to the Phantom Zone.  For his actions, or inaction, Zod regards Jor-El as a coward. Zod vows "..one day day we will return, and when we do I, will be Krypton's ruler.  And then...I will make you the slave to me that you are to the council. You will kneel before me.  Both you and one day... your son!"

Sentenced to the Zone

One Year Later

A boy crashes onto earth in a Kryptonian vessel, mirroring Superman's own origins. Superman is relieved that yet another survivor of Krypton has surfaced, but the child's origins are not so innocent.  The child is the son of Ursa and General Zod, the most dangerous criminals within the Phantom Zone. The boy's appearance on earth has triggered the promised return of Zod, Ursa and Non.  Upon their escape from the Phantom Zone, Zod and the others go to the Fortress of Solitude to gain information from Jor-El's recordings.  They then journey to Metropolis. 

Arriving in Metropolis, Zod sets about making his plans for Earth, or New Krypton, a reality.  While his wife, Ursa confronts Lois Lane to retrieve their son, he takes Non and confronts Kal-El.  Zod and Non are able to overpower Kal and trap him in the Phantom Zone, a fitting punishment in Zod's eyes.  Zod then freed the other criminals of the Phantom Zone, setting about re-creating Metropolis and Earth in Kypton's image.  With the aid of only a few Kryptonians he is able to defeat the Justice League and subjugate the people of Metropolis.  While he is attempting to discipline Lois, his son Lor steps in on her behalf, attacking him. At the same time a newly freed Kal-El teams with Lex Luthor and his Superman Revenge Squad to defeat him and the other escaped criminals.  As Zod battle Kal-El, Luthor manages to use Phantom Zone rockets to blast every being whose ever come into contact with it, including Superman, back.  While Kal is spared when Lor willingly takes his place, Zod is pulled into the Zone.  As he dissapears he mentions the other "horror" held in the Zone and promises to unleash it when he escapes again.  Zod plans to continue with his vow, and soon he will personally make Kal-El kneel before him.

New Krypton

When the bottle city of Kandor, the true Kryptonian Kandor, is found by Kal-El and released on Earth there are over 600 soldiers loyal to Zod numbered among them.  Two of those soldiers, Commander Gor and Lieutenant Mur, have trouble believing that Zod betrayed Krypton, and feel he was justified in his actions.  They also have trouble understanding why Kal-El stopped him. They decide to free him from the Phantom Zone, entering the Fortress of Solitude only to be stopped by a new Nightwing and Flamebird.

Alura though, had made a pact with Commander Gor and the rest of his millitary faction regarding the release of Zod and his followers from the Phantom Zone.  At some point during the events following the death of her husband, Alura made good on that promise, releasing Zod, Ursa, and Non from captivity.  Unbeknownst to the general populace of Kandor, Zod became the true power behind their forces and as New Krypton settled into it's orbit around Sol, Zod prepared to reveal his presence to his people. Superman eventually get's pulled into the conflict with Earth. However, General Zod accuses Kal-El and Asha Del-Nar of treason, when they refuse to execute a criminal. As the trial is going on, Dyn-Xe tries to argue that Zod has a personal vendetta against the House of El. Much to the dismay of Dyn-Xe, Kal El pleads guilty and had to wait a day to be judged. Zod offers to allow Kal to escape but he does not. On the day of judgement, Zod tells the judges that Kal should be cleansed from his sins on the account of Nova, by the Religious Guild. Kal is cleared from his charges, and at the next day at the parade, Kal and Zod are joined by Alura and Kara. A Kryptonian by the name of Ral-Dar rushes through the crowd and fires a weapon at Zod, possibly leading to his death. Almost dead Zod makes Superman the new General in charge of New Kryptons Military Guild.

Superman: The Movie and Superman II

General Zod was responsible for Krypton's defenses, but secretly conspired to overthrow the Kryptonian council and replace it with his own.  For his crimes, Zod was sentenced to the Phantom Zone with 2 of his followers, Non and Ursa, and vowed to avenge his imprisonment, assuring Jor-El that if he did not join with Zod, he or his heir would one day kneel before him.

When Zod, Non, and Ursa are freed and arrive on Earth, they battle with Kal-El as a means of settling their vendetta with Jor-El, as well as attempting to take control of Earth.  Superman is able to neutralize their powers at the Fortress of Solitude.  
 
In the movie General Zod was played by Terence Stamp.
 

Smallville

Superman: Last Stand on Krypton

 
In this Elseworlds sequel to Superman: Last Son of Earth, the High Council of Krypton asked Im-Zod to be their new general, to fight Jor-El and his movement against the established Kryptonian society. This version of Zod was killed by Lex Luthor.