Much like awards or commendations every army also has had similar problems with things like insubordination, desertion and even mutiny. During the Republican era, the discipline of the Legions was more strict and harsh than in the Imperial era.
This may be the result of several factors, including the volunteer nature of the Imperial Legion. More likely to be of influence was the Emperor's need to keep the army loyal and happy to preserve his position, or just the simple fact that as generations passed people were more lenient than they were in earlier eras.
Some simple disciplines and descriptions as warranted
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). They are all equal enough to any punishment in a modern army and self-explanatory in the cause and effects both on the individual and overall moral and discipline of the ranks.
Execution The death penalty was a rarely used deterrent used against desertion, mutiny or insubordination. In cases where execution might be considered, factors such as the soldier's length of service, his rank, previous conduct, soldier's age, etc. were taken into account. Special consideration was also given to young soldiers.
Decimation An extremely rare style of the execution penalty was called decimation and would only be used in extreme cases of cowardice or mutiny. Every tenth man of a centuria, cohort or even the entire Legion, randomly chosen by a draw of lots, was killed by being clubbed or stoned to death by the other members of his unit. The effect could be overwhelmingly positive or an absolute disaster.
Disbandment An entire legion could be disbanded without the customary land settlements and pension disbursements. This like the others was rarely done and was more likely as a deterrent to Legions who may be loyal to a political opponent or group. But the threat of being disbanded was sometimes used against troops with other more common issues but was rarely actually practiced.
For example, Legio I Macriana Liberatrix ("Macer's Liberators"), was formed by Lucious Clodius Macer, rebellious Governor of Africa, in 68 AD, to be used against Nero. In the midst of this year, that came to be known as the Year of the 4 Emperors, Galba was one of the men who took claim to the throne. Galba, distrusting of Macer's intentions ordered the death of Legio I's commanding officers and the disbandment of the questionably formed Legion. It was removed from service to the empire without ever seeing action.