Montesquieu wrote that "the main reason for the Romans becoming masters of the world was that, having fought successively against all peoples, they always gave up their own practices as soon as they found better ones."
Roman organization was more flexible than those of many opponents. Over time, the legions effectively handled challenges ranging from cavalry, to guerrillas, and to siege warfare.
Roman discipline (cf. decimation (Roman army)), organization and systematization sustained combat effectiveness over a longer period. These elements appear throughout the legion in training, logistics, field fortification etc.
The Romans were more persistent and more willing to absorb and replace losses over time than their opponents. Wars with Carthage and the Parthians and most notably, the campaigns against Pyrrhus of Epirus, illustrate this.
Roman leadership was mixed, but over time it was often effective in securing Roman military success.
The influence of Roman military and civic culture, as embodied particularly in the heavy infantry legion, gave the Roman military consistent motivation and cohesion.
Strict, and more importantly, uniform discipline made commanding, maintaining, and replacing Roman legionaries a much more consistent exercise.
Roman military equipment (cf. Roman military personal equipment), particularly armor, was more withstanding and far more ubiquitous, especially in the late Republican and Early Imperial era, than that of most of their opponents. Soldiers equipped with shields, helmets and highly effective body armor had a major advantage over warriors protected, in many cases, with nothing other than their shields, particularly in a prolonged engagement.
Roman engineering skills were second to none in ancient Europe, and their mastery of both offensive and defensive siege warfare, specifically the construction and investiture of fortifications (cf. sudis, castra), was another major advantage for the Roman legions.
Roman military training focused on the more effective thrusting of the sword rather than the slash.