The Military Oath

To be placed on the rolls of the legion, a recruit had to swear the military oath.
The oath, the sacramentum, naturally changed in time as the Roman state and the empire evolved.
In republican times, one man would recite the oath out loud (praeiuratio), thereafter each oteh man in turn would say the words, 'idem in me' ('the same in my case').
It may well have been that new recruits who joined the army all had to speak the full oath, if numbers allowed this. But the renewal of the oath, will have been conducted in the shorter fashion described above.
In early republican times, the historian Dionysius tells us, the oath sounded something like this;
'to follow the consuls to whatever wars they may be called, and neither desert the colours nor do anything else contrary to law.'
The renewal of the oath was always conducted on New Year's Day, up until either the reign of Vespasian or Domitian when it was moved to 3 January.

A Christian version of the oath is described by the historian Vegetius,
'They swear by God, by Christ and by the Holy Spirit; and by the majesty of the emperor, which, next to God, should be loved and worshipped by the human race... The soldiers swear to perform with enthusiasm whatever the emperor commands, never to desert, and not to shrink from death on behalf of the Roman state.'

Army Discipline

The discipline of the republican army is legendary. However, it is believed to be somewhat exaggerated by Roman historians keen to show that discipline of earlier generations had been firmer than that of their own.
Though it was indeed the case that a strict system of rewards and punishments was applied the the conscripted soldiers. But discipline was not necessarily so strict as to blunt the citizen-soldier's individual initiative. Intelligent, independent-minded soldiers who worked together as a unit no doubt posed a significantly greater threat to an enemy, than blindly obedient men who only did what they were told.
But then this is not to say that the discipline of the Roman army wasn't an iron one. During times of crisis such as the war against Hannibal severe measures were most likely necessary to maintain army discipline against a seemingly invincible opponent.
The historian Polybius reports that the Roman army punished with death not only things such as desertion but also far more minor matters and that order and discipline was largely maintained by fear.
In the days of the empire discipline does appear to have relaxed at least slightly. Perhaps this was due to it by then being a volunteer army which shouldn't be abused quite as harshly if one wanted to find any new recruits, perhaps it was the emperor's desperate need to keep the troops happy if he was to survive, or perhaps it was simply the result of changing attitudes of the day.
In any case the changes brought about more self-confident armies, which were more likely to revolt if an old-fashioned disciplinarian took command.

Corporal punishment (castigatio), monetary fine, (pecunaria multa), added duty (munerum indictio), relegation to an inferior service (militiae mutatio), reduction in rank (gradus deiectio) or dishonourable discharge from service (missio ignominiosa) were all forms of minor punishments at the disposal of commanders seeking to maintain discipline. Execution - The death penalty was a deterrent used against desertion, mutiny or insubordination. In practice however, it was rare. Even in cases of desertion, factors such as the soldier's length of service, his rank, previous conduct, etc. were taken into consideration. Special consideration was also given to young soldiers. After all, trained soldiers didn't grow on trees. To kill off one's own ranks was to be avoided as much as possible.
Decimation - Perhaps the most gruesome punishment of all known to the Roman army was that of decimation. It generally was applied to entire cohorts and meant that every tenth man, randomly chosen by a draw of lots, was killed by being clubbed or stoned to death by his own comrades. This form of punishment of the troops was however extremely rare.
Disbandment of an entire legion was also a means by which to punish mutinous troops. This naturally was very rarely done, and if so more for political purposes (ridding oneself of armies who had supported a contender to the throne, etc) then as a purely punitive measure. But the threat of disbandment was sometimes used against troops demanding more pay, or better conditions to bring them to heel.

Army Decorations

Like most modern armies, the Roman army did not only have a code for disciplining soldiers, but also one for rewarding them. Decorations were usually worn by the soldiers on parades and were generally awarded at the end of a campaign.

The decorations possible for any soldiers lower than the centurions were torques (necklaces), armillae, (armbands) and phalerae (embossed discs worn on the uniform).
Such minor awards were abandoned during the reign of emperor Severus, but the torques were reintroduced in the later empire.

Centurions could be awarded the corona aurea, a plain gold crown. Aside from this there was also the corona vallaris or corona muralis, for being the first officer over enemy defences or city wall.
(The corona aurea could apparently also be awarded to ranks beneath the centurionate, the little known so-called evocati who ranked between the principales and the centurionate.)

The primus pilus, the highest ranking centurion of a legion, could be awarded the hasta pura (silver spearshaft), which was the award usually handed to any members of the questrian order, - a rank the primus pilus would only strictly speaking have achieved by the end of his service.

Above the rank of primus pilus the awards become, just as the posts were, of more politically symbolic nature. High ranking commanders needed hardly storm any enemy walls in person to gain their awards. And it is to a point questionable if only truly oustanding commanders received awards.

A military tribune of the lowest rank (tribunus augusticlavius) would be awarded with a corona and a hasta pura. But those tribunes senior two him might already receive a vexillum. This award was a little miniature standard mounted on a silver base.
The senior tribune (tribunus laticlavius), a man of senatorial rank no less, would generally receive two coronoae, two hasta purae and two vexilla.
Men of praetorian rank, the legionary legates (the generals of the Roman army), would receive three coronoae, three hasta purae and three vexilla.
If this bestowing of glory in such numbers seems a little ridiculous, then it is still not the highest award. For a general of consular rank, would receive four coronae, four hasta purae and four vexilla.

An award which was open to all ranks, was the corona civica. It was an award granted for saving the life of a fellow Roman. Though it appeared to go out of use after the reign of Claudius. Emperor Severus later reintroduced it as the corona civica aurea, but only for centurions.

There is a wellknown case in the traditional Roman semi-mythical hero L. Siccius Dentatus of awards being quite literally heaped onto war heroes. A veteran of 120 battles he is supposed to have received 18 hastae purae, 25 phalerae, 83 torques, over 160 armillae, 14 coronae civicae, 8 coronae auraea, 3 coronae murales and one corona obsidialis/corona graminae (the highest award for valour).

But not only individuals, also entire units could be awarded. Praetorian cohorts could be awarded the cornona aura, which they could add to their standards. The regular legions could be granted a corona, but their cohorts could only receive phalera.