House Harkonnen was a Great House during the time of the Padishah Emperors. Home planet of House Harkonnen was Giedi Prime, a heavily industrialised planet with a low photosynthetic potential.
The Harkonnen name is believed to originate in what was western Russia on ancient Earth, and the region of Earth called Suomi, also Finland. It has been suggested that the Harkonnen name comes from Sweden as a derivation of Hakkon - but it is likely that it is indeed from Finland, as Härkönen is a 20th-century Finnish name.
The Harkonnen family during the time of the League of Nobles maintained a burgeonning commercial empire, and owned mining operations on the planet Hagal. The patriarch of the family, Ulf Harkonnen, and his wife, Katarina, were caught by Cymeks in their starship, above the planet Caladan. Piers, a son who accompanied them, was ejected down to the planet's surface, was never heard from again, and was presumed dead.
His brother, Xavier Harkonnen, was raised by adoptive parents of the Tantor family, Emil and Lucille, on the League capital world of Salusa Secundus. Xavier eventually became a Primero during the Butlerian Jihad, but was disgraced when he killed Grand Patriarch Iblis Ginjo, in the Thalim system.
Xavier's grandson, Abulurd Harkonnen, came to be the founder of House Harkonnen. The long-running feud with the Atreides originated after Abulurd refused an order from Vorian Atreides, to kill the millions of humans enslaved by the thinking machines. Abulurd's disobedience was exposed by Vorian himself at the Battle of Corrin, the Jihad's last battle. As a result, Abulurd was labelled a coward and a traitor. He was banished from the League Worlds to the frosty planet of Lankiveil by his own brother, Faykan Corrino, who became the first Emperor. Abulurd's sons were told this story, and grew hate about the name Atreides, and all their descendants.
House Harkonnen in the times of the Padishah Emperors was most famous for its underhanded and sinister political tactics, and for an ancient feud it maintained with another Great House, House Atreides. In addition, House Harkonnen had a reputation for ambition, malevolence, hatred and brutality. It was typically ruled by a Siridar Baron.
Emergence as a Great House
After many centuries toiling as a House Minor, Harkonnen influence gradually rose within the Landsraad, due mostly to shrewd manipulation of the whale fur market, which was primarily the efforts of Baron Dmitri Harkonnen and his son Baron Vladimir Harkonnen.
Abulurd, Obeshev's son, disgraced the House's name because of his treachery in the Battle of Corrin, but his demibrother Ivan Harkonnen's line became Dukes of Eluzai. This line had members such as Saudir III and Saudir IV, usurpers of the throne until orphaned with the later's death.
For centuries thereafter, the Harkonnens, while not officially disgraced, they filled the role of businessman and planetary squire, and stayed out of Imperial politics. Count Abulurd III Harkonnen was stripped of his title twice and the Harkonnens were demoted to their lesser title of Lords Tupelo, and were required to pay a large fine into the Imperial treasury.
About the time Vladimir II Harkonnen became Duke of Chamizai the Harkonnens were first proposed for membership among the Great Houses; the Harkonnen family had always been enterprising, specializing in the trading of goods for profit, the renting of mercenaries, and the pursuit of exotic luxuries for the wealth. To translate these assets into power required political acceptance of their family as one of the elite. Vladimir Harkonnen persuaded Count Ernst von Wikkheiser to sponsor a resolution in the Landsraad proposing the Harkonnens as a voting house; the motion failed by a small number of votes when the Atreides spoke against it.
At the death of Emperor Henoor III in 1604 AG without immediate heirs, and at the verge of civil was, Abulurd VI Harkonnen planned to attack the Landsraad meeting site. Then the Atreides challenged him to kanly. Abulurd accepted the challenge, with the Imperium at stake, but was defeated. As a result, the Harkonnens were stripped of their titles and possessions, and exiled once again. Eventually they were restored by Corrin IV, who was enthroned by the machinations of Iraklii Harkonnen, after a period of tumult created by himself.
The House begun a conflict with House Pardee which was the first recorded instance of a war of assassins (3367 AG-3375 AG) after which House Pardee was virtually obliterated. Various stories attribute this victory to the defection of the steward of their rural estate, a jealous functionary who was easily bribed. Undermining the loyalty of the retainers of another house was a specialty at which House Harkonnen seems to have excelled, according to the reputation of the house among others.
In 10182 AG, Shaddam IV was said to have interfered in a War of Assassins between Houses Harkonnen and House Kalifi?, preventing the assassination of Baron Vladimir Harkonnen.
House Harkonnen had built its power on maximising production output, and minimising production expenses by ignoring economically ethical behaviour. Indeed, Harkonnen governing was based upon a simple foundation of fear and terror. They were used in governance, in the day-to-day running of the Harkonnen household, and in controlling the Harkonnen armies. With a social order based on treachery and punishment, soldiers rose through the ranks through deceit, trickery and, if necessary, assassination.
In approximately 10130 AG, House Harkonnen won the siridar fief of Arrakis. Their responsibility was to mine the spice melange and supply it to the universe. Through their persecution of the Fremen, and through the minimisation of outlay on infrastructure and pay, the Harkonnens managed to pay the tithe they owed to the Emperor, as well as keep a substantial amount of melange for themselves. By 10191 AG, the Harkonnens had managed to amass considerable wealth through spice mining.
Despite House Harkonnen's relative power prior to the end of the Corrino Empire, Vladimir Harkonnen desired the ultimate achievement of usurping the Corrinos and form the Harkonnen Empire. Thus, he secretly plotted against both House Atreides and House Corrino, hoping to destroy the former and overpower the latter through force and marriage.
However, Vladimir Harkonnen's plans were ultimately unravelled by the rise of Paul Atreides on Arrakis. After Vladimir Harkonnen's death at the hands of Paul's younger sister, Alia Atreides in 10193 AG, the title of Baron passed very briefly to his nephew, Feyd-Rautha Harkonnen, before being killed by Paul Atreides in an act of kanly.
After the ascent of House Atreides, what little remained of House Harkonnen saw its power and resources quickly disappear. Control of Giedi Prime was given the people of Caladan, and under the direction of Gurney Halleck, once a slave on that world, dismantled the machines of industry, changed its name and the names of its cities, and replanted forests and greenery there. House Harkonnen essentially ceased to be during the time of Muad'Dib's Jihad. However, the Harkonnen bloodline continued to exist through Bene Gesserit breeding programs for more than 1500 years thereafter.
The Counts Harkonnen-Rabban, generally known only as Counts Rabban, continued to survive as a House Minor for several hundred years into Leto II Atreides's reign, but gradually lost its noble status, along with the other Houses Minor. No mention of the Rabban name appears in local records after the year 10884 AG.
Sources: Essentially all books about the Dune Universe.