Were slave armies used?

A famous example is the Spartan army whose large portion consisted of helots.

During the American Civil War, some, prominently Judah P. Benjamin, suggested that slaves be used in combat. But for both the obvious reason that arming slaves seems like a very dangerous thing to do and for the ideological reason that if slaves could make good soldiers then the natural superiority of Whites which justified slavery in the first place would be called into question.

Only when the South was in desperate straits was the use of slaves in combat explored -- I do not know if any were actually given weapons and you can bet that officers commanding slave battalions would be White; in any event, slaves never fought for the South in large numbers; slaves were used as labor to supplement White soldiers, digging ditches and also working in armament industry (Tredegar factory).

Source: Evans' bio of Judah P. Benjamin, The Jewish Confederate, is a good source about JPB's stance on usage of slaves by the South.

With a slightly broader definition of "slave" to include conquered peoples who were used as slave labor, we have the Osttruppen of the Wehrmacht (German Army in WWII) made up of soldiers from areas of Eastern Europe and the Soviet Union overrun by the Germans. Some were volunteers either pro-Nazi or anti-Stalin or just looking for a decent meal. Others were POWs conscripted or coerced into serving. By late 1943 there were almost half a million Osttruppen fighting for the German Army shoring up their ever increasing manpower shortages.

The most famous example in the West is the 439th Ost Battalion defending Omaha Beach on D-Day. Many surrendered as soon as their defensive position was compromised, while others were held at their posts by their German sergeants. Many Allied soldiers were surprised by "Germans" speaking Russian or Polish.

Slaves in the military were common in West Africa from at least the seventeenth century:

The most important privileged slaves in West Africa were the warriors....The number of slave warriors in western Africa grew during the seventeenth and eighteenth centuries. They served the state by fighting, but also by running messages, administering the court and holding important posts.

Samori Toure, founder of the Wassoulou Empire (1878-98), had an army which included around 30,000 infantry, most of whom were slaves. These male slaves were armed with

imported breech-loading rifles and muzzle-loaders manufactured by local blacksmiths.

In the Senegambia region of West Africa,

ordinary slaves were divided into two categories : slaves who had been captured during the countless raiding expeditions, and slaves bought at the slave markets. The former were kept in special villages both in time of peace and war. After several years in such villages the bravest of them were selected to become warriors, and were henceforth royal slaves. They would fight under the command of the chief, and he alone had the right to punish them.

Source: Mbaye Guerre, The slave trade within the African continent in UNESCO, The African slave trade from the fifteenth to the nineteenth century

The French also used slaves as soldiers in the French Sudan (now Mali) in the late 19th century. According to the French soldier Joseph Gallieni:

The enlistment bonus is 250 francs. If he is a free man, we give him the 250 francs and he serves you loyally. If he is a slave, we act as follows so as to not annoy the master: the master is told when the slave will receive his bonus and often he takes it and the slave has nothing.

Cited in Martin Klein, Slavery and colonial rule in French West Africa

Slaves were also used as soldiers in the Dutch colony of New Netherland around the mid 17th century:

The WIC [Dutch West India Company] enlisted its male slaves in military campaigns against the natives during the Indian war. These slaves did not bear firearms but instead wielded small axes and half-pikes.

Mamluks are the big example of historical slave soldiers, but a very big and often overlooked characteristic of mamluks is that they were bought as slaves but were freed before becoming full soldiers. You have slave recruits but manumitted full soldiers. As such it's more of a freedman army than a slave army.

Part of the idea was likely that the mamluks would feel obligated to the sultan because he manumitted them. Another part, I think, was probably the idea that if you import foreigners from far-off lands then they won't have any connections with the locals. It's harder to plot a grand conspiracy against the sultan when you're a foreigner and you don't know anybody.

The game of thrones version in which they're ultradisciplined supersoldiers doesn't always match history. In Egypt and Turkey these soldiers managed to achieve some mixed successes, but they acquired a poor reputation in most of the Islamic world as having poor morale and bad battlefield performance, and often were soldiers of last resort for a ruler who, for one reason or another, wasn't able to get enough free soldiers. Which is pretty much what you'd expect.

Last difference is that mamluks weren't bought and sold after they became soldiers, unlike in GOT. They were bought to recruit them, but after starting to train them as soldiers they weren't for sale. Nobody went around putting trained armies - supersoldiers or otherwise - on the auction block where a rival (or some random schmuck) could buy them.