Particularly during the rather piecemeal conquest of Britain, which at times became one-tribe-at-a-time, the Romans would "gift" a cohort of legionaries to a tribal ruler who agreed to submit to Rome to serve as their bodyguards. Of course, guarding the new puppet ruler was a secondary priority. Their actual role was to keep an eye on the new subjects of the Empire and crush any resistance before it truly had a chance to begin.
The Byzantine Empire followed the Roman tradition, hiring personal guards during its long history from such diverse foreign ethnicities as Armenians, Kievan Rus, Scandinavians, Anglo-Saxons, Normans, Sicilians, and Turks. The most famous of these cadres was The Varangian Guard, which was first recruited from the Rus and later became a favoured career option for Scandinavians. After the Norman conquest of England, many Anglo-Saxons who were unwilling to submit to Norman rule migrated to Byzantium and joined the Varangian Guard. Unlike the Praetorian Guard, they were notoriously loyal, but more to the position of Emperor than the individual (i.e. they'd try to stop any overt assassins, and never tried to assassinate an Emperor themselves, but if you succeeded in unseating an Emperor they'd serve your or your designated Emperor as well as they had his predecessor).
Medieval to early modern
The Keshik of the Mongol Empire were a diverse lot. Founded by Genghis Khan, Keshik were sworn to individual Khans, but not to the position itself. Because of this, each new Khan had to hire a new generation of Keshik. Genghis Khan's consisted of Han Chinese, Manchurians, Kazakhs, and fellow Mongols. Later Khans would hire an even more diverse array which at different points included Persians, Georgians, Armenians, Alans, Koreans, Italians, and Russians.
Gallowglasses (Irish *gall óglach*, literally "young foreign soldier") were originally Norse/Scots warriors brought to Ireland as mercenary regiments and bodyguards for Gaelic Kings and lords. As they settled in the country for generations and became an indispensable fixture of warfare, they became more of an elite class of heavy infantry, with many recruits being native-born.
The Ottoman Empire's Janissaries, who were Christian children enslaved at a young age from subject territories (mostly those in eastern Europe) and trained into elite military units. The system was engineered to create and ensure loyalty to the Ottoman Sultan alone and prevent the rise of a native military and bureaucratic aristocracy that could rival him. The several Janissary revolts happened once this way of recruiting loosened (as early as the end of the 16th century; it totally ended in the 18th). The Ottomans likely got this idea from the Ghilmans, slave-soldiers of Turkic origin used in Muslim Persia after the rise of the Abbasid dynasty, and the also-foreign-slave-soldier Mamluks of Egypt. Similarly to the Janissaries, these ended up laxing their standards and getting locals involved, got too much temporal power and rebelled against their rulers (or, in the case of the Mamluks, became the rulers).
In a subversion of the expectation that foreign troops would be above palace intrigue, in 1373 the ruling regent of Cyprus, John of Lusignan, Prince of Antioch, was convinced by his sister-in-law, Eleanor of Aragon, Queen of Cyprus, that his Bulgarian bodyguards were going to betray him, and had them all thrown off the highest tower of St. Hilarion Castle. Eleanor had him killed a very short time laternote John had been involved in the murder of his brother (and Eleanor's husband) Peter.
The Western Trope Codifier today is likely the Swiss Guards that protect The Pope in Vatican City, Rome. The silly pants may make them seem a little like Bunny Ears Lawyers, but they were a terror on the battlefield in the late 1400s to early 1500s, and they retain their tradition faithfully. And while they look silly, anyone trying to do harm to His Holiness will come to realize, to their detriment, that they are highly trained military professionals—they have all completed basic training with the Swiss Army, are chosen according to exacting standards of physical fitness, and are given further training once they arrive in the Guards. And although they are most often seen with their ceremonial weapons (swords and halberds) for guard duty and for the tourists, this is in reality their version of the 18th-century uniforms worn by the British Royal Guards; when actually guarding the Pope, they carry the standard-issue weapons of the Swiss Army: the SIG Sauer P220 handgun, the SIG SG 550 assault rifle, and the MP5 submachine gun … and they wear more practical, monochrome uniforms while at it.
King of Poland John Sobieski used former Janissaries taken as POWs as part of his Autorament.
The Walloon Guards, which protected the Spanish Bourbon monarchs from 1734 to 1820. They were drawn from the Walloon people of Belgium.
The Gardes-Suisses (Swiss Guards) of the French kings, including the more ceremonial body-guards, the Cents-Suisses (Hundred Swiss). During the The French Revolution they, unlike the Gardes-Francaises (French Guards), who sympathized with the Revolution, remained true to Louis XVI and were killed during the storming of the Tuileries in 1792.
The French monarchy also had the Garde Écossaise (Scots Guards), originally a company of knights and mounted archers part of a Scottish expeditionary force during The Hundred Years War that king Charles VII kept with him. With time they formally became his bodyguards, and, as their ranks were enlarged and filled with Frenchmen, became the first company of the Garde du Corps du Roi (Bodyguards of the King), the main cavalry regiment of the royal guard.
Napoleon's Imperial Guard included a squadron of Mamluks (the nucleus of which had been brought over from Egypt, although as time progressed more and more Frenchmen filled the ranks), a regiment of Polish lancers (raised in 1806/7), and a squadron of Lithuanian Tatars (raised in 1812). One squadron of Polish Lancers accompanied him to exile in Elba and later served in the Waterloo campaign.
Modern
During the Russian Civil War, the Red top brass was guarded by the Latvian Riflemen. Also, they got Chinese mercenaries — usually converted from workers who ended up "marooned" when the empire gone down. These were also used in the guards role. which later was codified as the special unit: "The First International Legion of Red Army".
During the Spanish Civil War, the Nationalists' regulares, colonial troops drawn from the native populations of Spain's North African colonies, so distinguished themselves in battle that after the war Franco formed a personal guard known as the Guardia Mora (Moorish Guard), who dressed in exotic native uniforms and rode white Arabian horses.
African mercenaries seem to be the personal choice of many dictators, when the loyalty of their own army becomes suspect. Due to the frequent wars and disintegrating states in parts of African many of these are quite experienced and well equipped.
The Presidential Guard of Gabon was staffed until the late 90s by veterans of the French Foreign Legion, particularly the disbanded 1st Parachute Regiment. One of them, Louis-Pierre "Loulou" Martin, served President Omar Bongo from 1967 to 1993.
Watchguard International (established by SAS founder David Stirling) used to supply ex-SAS and British military bodyguards for African and Arabian leaders. The suggestion has been made that this was an unofficial means of maintaining a British presence in former colonies who might find it politically unacceptable to ask for British military aid.
The Middle Eastern Trope Codifier may be the Circassian Guard which protects the King of Jordan. They are drawn from the Circassian people, which originate from north of the Black Sea before being scattered from their homeland. They continue to wear colder-climate uniforms, including wool hats, leather boots, and capes while guarding the kings of the desert country.
Two-Gun Cohen, the Polish-born British, Canadian, and Jewish bodyguard to Dr. Sun Yat Sen.
, a cadre of Germans (from outside the borders of The Roman Empire) whose job it was to guard the Julio-Claudian emperors. The most important thing they defended them from was the Praetorian Guardnote . Yes, the early emperors of Rome had a group of bodyguards whose job it was to protect them from their own bodyguards.