Praetorian Guard

The praetorians (cohors praetoria) were the imperial guard to protect Rome and the emperor. They were a crack unit whose members wore a special uniform and received double pay, in addition to the bribes which they came to be offered in the guise of bonuses for their allegiance.
(Traditional teaching is that the praetorians were crack soldiers, chosen for their fighting ability. There are however those who claim that the Praetorian guard, rather than being a body of select men, were merely an army drawn from Italy, rather than from the provinces.)
When the emperor went on campaign, the imperial guard went with him.
The institution of the cohors praetoria had originally been that of a group of men acting as bodyguards to a general, but Augustus - most likely drawing on the experience of Julius Caesar's murder - created a large personal army.
Initially, the Praetorian guard consisted of nine cohorts of 500 men each. This was increased by emperor Caligula to twelve cohorts. Vitellius again increased their number to sixteen cohorts. Vespasian therafter reduced their number again to nine cohorts and Domitian increased them to ten cohorts of 500 men. A cohort was commmanded by a tribune, together with two equestrians.
The guard itself was commanded by the praetorian prefects, who were equestrians rather than of senatorial rank. A sign of the exclusion of the mighty senate from certain key positions by the emperor.
Soldiers of the praetorian guard served only for sixteen years, a term much shorter that the service of an ordinary legionary. But after their sixteen year term they became so-called evocati, which ment that they were held back from discharge. Their service in the praetorians meant they either went on to perform specialist military duties or it simply qualified them either for service as centurions. These centurionates would usually be taken up in praetorian guard itself or in the city cohorts and the vigiles. Though some also took commands as centurions in the regular legion.

Imperial Horseguard

Together with the praetorian infantry unites there was also a small cavalry unit, which by the second century - created either by Domitian or Trajan - had become the imperial horseguard (equites singulares augusti). This cavalry unit, drawn from the best frontier cavalry forces, was in size about that of a ala quingenaria which would amount to roughly five hundred men.
Unlike the praetorians, the imperial horseguard did not necessarily wear special uniforms or insignia. Instead every rider may well have worn his individual provincial equipment, thereby granting the unit a very cosmopolitan appearance, reflecting the variety of people within the empire.

The early emperors tried their best to detract from their reliance on the military, choosing to be seen as political leaders instead. So the praetorians and the imperial horse guards often wore civilian clothes in those early days.

The German Bodyguard

The German bodyguard (germani corporis custodes) was reasonably small unit of up to 300 men, which formed a guard around the emperor, closer still than the praetorians. Being foreigners, almost entirely recruited from the German tribes of the Batavii and Ubii, they were seen as less corruptible by bribes of power or privilege than the praetorians. Though it was exactly their foreign blood which also made them very unpopular.
They existed only under the early emperors, commanded by the emperor himself, until in AD 69 Galba disbanded them.

The Palatini

Among the many reforms introduced by Diocletian one was the creation of a huge imperial guard. He confined the Praetorian Guard (which he saw as corrupt and dangerous) to Rome.
The numbers of the new troops he originally raised, the palatini, are not known. But by the end of the fourth century this new imperial guard mustered twenty four vexillations of cavalry (five hundred each), twenty-five legions (a thousand each) and one hundred and eight auxiliary troops (five hundred each), stationed all around the empire at the major cities.

The Varangian Guard

The Varangian Guard, also known as the Waring Guard or the Barbarian Guard, emerged in the 11th century in Constantinople as the bodyguard to the emperor. The first mention of this guard appears in 1034, and they were re-organized in the mid eleventh century by Romanus IV.
Mostly this bodyguard consisted of Danes and Englishmen, many of the latter joined after the defeat at Hastings in 1066, preferring the service to the emperor to life under Norman rule back home in England.
The Varangians were ferocious fighters, with full beards and using two handed battle-axe as their prefered weapon (which is why they were also known as 'the axe-bearers' in Constantinople). They lived under their own laws, prayed at their own church and elected their own officers.
Their leader was known as the 'Acolyte' (the follower), which was derived from the fact that he always followed immediately behind the emperor whereever he went. At banquets or audeniences the acolyte was to find found standing right behind the emperor's throne.
Unlike bodies such as the Praetorian Guard, the Varangians became famed for their loyalty to the emperor, even their willingness to fight to the death to protect him.

City Cohorts

Towards the end of his reign emperor Augustus created three more praetorian cohorts, bringing the number to twelve. But these additional cohorts were very soon re-designated as city cohorts (cohortes urbanae). Their duty was to patrol the city of Rome as a police force.
Given their success, further such cohorts were formed and sent to police other important cities of the empire.

The Vigiles

A further force, the vigiles, also created by Augustus patrolled Rome itself and served as its fire brigade.
Seven cohorts of 1000 men, all recruited from former slaves, were established. The whole force was commanded by a praefectus, and each cohort in turn was commanded by a tribune.
The vigiles carried quite sophisticated fire fighting equipment, including water pumps and hoses, and even ballista catapults with which to fire hooks attached to climbing ropes or to demolish burning buildings in order to prevent the spread of fire.
It is believed that they wore helmets for protection, but it is unlikely they wore any other kind of armour. Although they were indeed understood to be a military unit.
Centurions for the vigiles appear to have been drawn exclusively from the praetorian guard.

Allied Troops

The realms of so-called 'client kings' were largely seen as an extended part of the Roman empire. Very often these royal houses owed their position to Rome. As part of the arrangement between Rome and the client kingdoms, the kings had to provide troops for Roman campaigns. It was therefore not uncommon for the troops of such client kings to fight alongside Roman forces in battle against the enemy.
For example Titus' army in Judaea in AD 70 was accompanied by forces of Agrippa II (Palestine), Sohaemus (Emesa) and Antiochus IV (Commagene).
Some of the troops from these client kingdoms were even trained in a fashion similar to that of Roman legions, in order to be more effective on the battle field when working in union with real Roman forces.
For instance the annexation of Galatia as a Roman province brought the thirty cohorts of King Deiotarus under Roman command and saw them formed into a Roman legion (legio XXII). Though this was clearly an exception. The vast majority of troops from annexed client kingdoms became auxiliary forces.