Slavery, as Paul LeVal wrote in 1861, was "one man owning another". (PROSE: Blood and Hope) Often, but not always, the enslaved were "different" than their their oppressors. In LeVal's day, the basis of slavery was "skin colour or land of origin", but off Earth, one species sometimes enslaved other species.
Humans and slavery
Humanity had a long and largely unhappy relationship with slavery. Sometimes other species enslaved humans, but there were many examples of one group of humans enslaving another, or of humans enslaving other species.
Other species enslaving humans
Daleks forced many people into labour in Bedfordshire, (TV: The Dalek Invasion of Earth) as well as on Skaro itself. (TV: Destiny of the Daleks) and on the planet Nixyce VII. (AUDIO: The Traitor) They also occasionally enslaved humans through physiological manipulation, such as when they created robomen or "humanoids". (TV: The Dalek Invasion of Earth, COMIC: The Humanoids) The Cult of Skaro once attempted to actually blend Dalek and human DNA to create a more reliable class of slave labour. (TV: Evolution of the Daleks)
At least one Time Lord — the Master — enslaved humans on a massive scale. Through fear alone, he got virtually the entire population of 21st century Earth to help him create what he termed "the New Time Lord Empire", a project that involved massive building works all around the planet. (TV: Last of the Time Lords)
Humans enslaving humans
Humans used other humans as slaves for centuries. Every culture, the world over. Nobody ever challenged them until a few hundred years ago. And in some places it still goes on.
The Romans enslaved other people. Both Ian Chesterton and Barbara Wright were sold into slavery. (TV: The Romans) Centuries later, humans like Doland looked favourably upon the Roman Empire's use of slavery. (TV: Terror of the Vervoids)
Slavery of Africans was institutionalised in the United States of America, enshrined in the Constitution of the United States. However, the nation was deeply divided on the issue, and there was a tenuous balance between those people — typically in the North — who wanted it abolished and those — often in the South — who saw slaveholding as a moral right. This tension finally exploded into the American Civil War. South Carolina, the first state to secede from the US, justified its action in a declaration which clearly cited US President-elect Abraham Lincoln's hostility to slavery as a main cause for secession. Since secession directly resulted in war, slavery was a central reason the war was fought. The eventual victory of Lincoln was something the Fifth Doctor, Peri Brown and Erimem were on hand to witness — although Erimem was sometimes unpleasantly mistaken as a slave because of her darker skin. (PROSE: Blood and Hope)
Likewise the English enslaved the Scottish during the mid-18th century. People like Solicitor Grey and Annabelle captain Trask routinely forced Scots from the Highlands to the West Indies and North America. They attempted to give it the veneer of legal propriety by having each Scot sign a contract, whereby their labour was exchanged for the "privilege" of ocean transport to their new "home", but these signatures were effectively coerced. Clearly, the Second Doctor and Ben Jackson saw it for the slavery it really was. The Doctor, in fact, deprived Grey of his contracts for one particular voyage, thereby removing even the veneer of propriety from Grey's activities. (TV: The Highlanders) Indeed, Grey himself privately confided to his co-conspirators that he knew very well he was sending the Highlanders into slavery, saying to Trask, "But to take these cattle fresh to the slave plantations — before their health has been sapped by His Majesty's prisons — that takes skill and preparation." (PROSE: The Highlanders)
Other parts of the world were involved in the slave trade, as well. The Fifth Doctor once told Turlough that he recalled seeing slave ships in the harbour at Rio de Janeiro in 1700. (AUDIO: Loups-Garoux)
Humans enslaving other species
It was certainly Doland's intent to turn the Vervoids into slave labour. Had he been able to deliver the sentient plants to Earth, he intended to use them as cheap replacements for robots. He didn't know, however, that the Vervoids themselves had the ability and desire to kill every bit of animal life they encountered. (TV: Terror of the Vervoids)
As Rose Tyler observed, humans enslaved the Ood in her far future. Even in remote outposts, some humans, like Danny Bartock, were charged with keeping order amongst the Ood by using a variety of technological devices, such as those which measured Basic, a scale for determining the level of Ood telepathic output. (TV: The Impossible Planet) This level of technological and manpower specialisation suggested a systemic and institutionalised form of slavery.
As Donna Noble would later discover, the humans of the 42nd century had industrialised and commercialised Ood slavery. By 4126 Ood Operations, the company in charge of the Ood, were having difficulties in the vast marketplace of the Second Great and Bountiful Human Empire. They began a new, aggressive advertising scheme that year which slashed prices, added "extra features" to the translator balls and generally attempted to "rebrand" Ood with Ood Operation's dealers. Donna and the Tenth Doctor were repulsed by this blatant commercialism. Together, they helped the Ood revolt and end human Ood trafficking. (TV: Planet of the Ood)
Tharils were traded by the humans because of their time sensitivity, used to pilot ships in the fourth dimension. Romana devoted herself to overthrowing this commerce. However, in a previous age, the roles had been inverted: humans had been enslaved by the Tharils themselves as servants. (TV: Warriors' Gate)
Slavery between non-humans
Slavery was hardly a phenomenon exclusive to human culture.
The Sycorax likely practised slavery. During their invasion of Earth on Christmas Day, 2006, they planned to sell half of humanity into slavery. (TV: The Christmas Invasion) This suggested that not only were the Sycorax morally unopposed to slavery in general, but that there was some sort of market for slaves well beyond the confines of the planet Earth.
Huducts enslaved Anubians by using mind-controlling torcs. After the Anubians were liberated by K9 Mark I, the Anubians turned on their former masters and enslaved them in the same way, even though K9 intended for them to reconcile in peace. The Anubians later developed space travel and enslaved other species. (TV: Curse of Anubis)
The Mentors from Thoros Beta took many Thoros Alphans from their homeworld for use as menial labour and experiments. Thanks to the intervention of Yrcanos and the Sixth Doctor, the control centre which let them to be enslaved was destroyed. (TV: Mindwarp)