The Praetorian guard had a tendency to assassinate emperors they did not like. Any guard formed out of Roman citizens would have a personal interest in the way the empire was being managed and could not be trusted with the life of the man responsible. If they did not like how the empire was being run they could easily remedy that by killing the man in charge and picking someone else. As a result emperors would use men that had no interest in the politics of Rome as their personal guard. These men were hired from German auxiliaries and were considered very loyal because they were foreign. There is not much information regarding the more specific aspects of this guard. It's assumed that their unit size was around 400 men and they would use Batavians a lot because of their reputation for being brave and their physical prowess. They were first mentioned by Julius Caesars in his commentaries. Later by Suetonius in his account of Caligula, twice, and Galba who disbanded them in 68ad.

Edit: some commas

Edit2: This link better shows the introduction of German cavalry into Caesars army.

Edit3: I keep thinking of things. This is the last one though. If you feel like reading about Germanic tribes during the time period from one Romans point of view I would recommend Germania, by Cornelius Tacitus. A very interesting read and it's pretty short.

You are referring to the Germani Corporis Custodes; the German Guards.

There are a few reasons the German and Gaulic tribes were chosen:

• The German and Gaulic tribes had proven themselves incredibly fierce opponents during previous Roman expeditions. Roman Legion auxuliaries, comprised of various non-citizens, often included men from the tribes that submitted to Roman authority. A famous one would be the Batavian Horse; an auxuliary cavalry unit originally comprised of Batavian horsemen, famed for their ability to ford rivers while mounted on their horses and procede to fight. Their loyalty was steadfast (there would be revolts cause by Batavi, such as the Civilis revolt, but even then the Batavian Horse did not join their Batavian bretheren) and they were well regarded by most of the Legions for their skill. Of course this is, but one such a unit, there were many other auxiliaries, not as famous, but just as well regarded as soldiers.

• They weren't Roman, and this is perhaps one of the most important things about them; like the Varangians were bodyguard to the Byzantine Basileous because of their disinterest/unfamiliarity with local politics, not to mention battle prowess, so too was the German Guard relatively disinterested in Roman politics. They were NOT citizens. As history would show, the Praetorians overthrew or killed Roman Emperors rather often; the German Guard only overthrew one Emperor: Caligula did not kill a single Emperor (thank you for the correction /u/AnOddOtter and /u/Agent_Sean). When the Emperor Vitellius was being overthrown by Vespasian, three cohorts of the German Guard stormed the Senate and killed Vespasian's brother, Sabinus, and then fought to the death for their Emperor, Vitellius.

Of course there were a few occasions when the German Guard was ostracized: after the Teutoberg Forest Disaster (9 AD), Augustus temporaily disbanded the German Guard, due to a mistrust of them, using the Praetorians as his close bodyguard.

In any case, the German Guard lasted until 69 A.D. when Vespasian disbanded them in favor of the Praetorians

(As my source does not back this statement up with direct evidence, I must default to the position presented by Agent Sean above: the German Guard was permanently disbanded by Galba. If anyone would like to view the claims exact words, I have posted an imgur link with the pertinent statements in a comment below).

There were and would be other non-Praetorian bodyguards among the Roman Emperors such as the Imperial Singularian Horse (Latin name: Equitum Singularium Augusti) which was originally comprised of vaunted German cavalrymen and formed by Otho. Their first real battles were under Vespasian and they helped put down the Civilis revolt.

Let me know if you'd like a bit more information on anything.

EDIT: Source:

"Legions of Rome: The Definitive History of Every Imperial Roman Legion", Dando-Collins, Stephan

The Romans had a war culture centered around the competing ideas of disciplina and virtus. As the Roman citizens grew more civilized they lost virtus in their own eyes and began seeking it out at the fringes of their empire. At this time the Germanic tribes were on the fringe of the empire and so were a prime candidate for virtus recruitment. Thus both the praetorians and legion got Germans.

Source: Soldiers and Ghost by John Lendon and his class Greek and Roman Warfare.