The Romans, as a rule, did not go conquer new people they met for no reason. They always tried to justify their wars to themselves, even if we might see some of those justifications as spurious or self-serving. When Romans did wage wars that were seen as unjust, this met with pushback politically, or even from the soldiers themselves. Consider this passage describing Caesar's wars in Gaul, when he decides to attack a Germanic people from across the Rhine:

Meanwhile reports reached the soldiers that Ariovistus [The Germanic leader] was making vigorous preparations, and also that many other Germans had either already crossed the Rhine to assist him or had collected on the very bank of the river to attack the Romans suddenly; hence they fell into deep dejection. Alarmed by the stature of their enemies, by their numbers, their boldness, and consequent ready threats, they were in such a mood as to feel that they were going to contend not against men, but against uncanny ferocious wild beasts. And the talk was that they were undertaking a war which was none of their business and had not been decreed, merely on account of Caesar's personal ambition; and they threatened also to desert him if he did not change his course. - Cassius Dio, Roman history 38.35

Emphasis mine. We likewise find examples of Crassus adventurism against the Parthians being condemned, as well as lesser known earlier examples like condemnations of Manlius Vulso's attack on the Celts of Asia minor in 188 B.C. Warmongering was not seen as a positive trait for Romans.

That said, Romans had a very different world-view from our own. When they did have a justification (an enemy king supporting raids into their territory or harbouring pirates, one of their allies being threatened, a migration threatening to destabilise a region) they would wage war with ruthless brutality and would consider their conquest of these peoples to be a good thing. Any attempt by the conquered to then throw off the Roman yoke would be seen as treason and rebellion, and punished accordingly.

Like the Spanish conquerors, the Romans would also use (alleged) barbaric habits by their enemies as justifications for the rightness of their cause. Famously, they condemned the Carthagians and Druids for practicing human sacrifice, and used that as part of their justification for their wars. (Nevermind that the Romans themselves occasionally practiced human sacrifice themselves, including as late as during Hannibal's invasion of Italy.)

Of course, the justification the Romans offered and the realities on the ground may have been two quite different things. There has been quite a vigorous debate amongst historians over the decades on the actual reasons for Roman expansion and imperialism. Some historians have sought to paint Rome as calm and reasoned statesmen, who acquired their empire solely in self defense. (A perspective that, unsuprisingly, was quite popular among historians living in European imperalist powers of the 19th and 20th century.) Nowadays it is more common to see them described as singularly aggressive conquerors who came to dominate the Mediterranean by virtue of being more ruthless than anyone else. (e.g. Harris, War and Imperialism in Republican Rome, 1979)

I rather like Arthur Eckstein's attempt to place Roman expansionism in the context of the realist school of international relations. According to this line of thought, city-states in the ancient world had a precarious and uncertain existence. War was common, justifications were easily found, and most any city state might find itself conquered and enslaved or destroyed by a more powerful neighbour at any given moment. Indeed, the early history of Rome itself sees the city subjugated by the Etruscans and sacked by the cisalpine Gauls. In order to protect themselves in such a dangerous world, city-states were all very aggressive and militarised, they would all seek to gain more power (and thus more security for themselves) by conquering weaker neighbours, and seek to make alliances for protection with stronger powers. In such a world, war was normal, and it's not really necessary to try very hard to explain it.

Of course, at a certain stage Rome was by far the biggest fish in the Mediterranean pond, and its own existence wasn't directly threatened that often. (Though the Romans themselves did not necessarily see it that way, witness the reactions they had to the Pannonian revolt just across the Adriatic as late as the reign of Augustus.) But here is an interesting twist in this framework of interpretation: rather than looking at the actions of the big power in the centre (Rome) we can look at the actions of the smaller powers on the periphery.

When you are a small power whose existence is threatened by your neighbours, it makes perfect sense to seek the protection of a nearby superpower such as Rome. But doing so might encourage your enemy to seek the protection of a rival superpower. (such as Carthage.) This then draws the greater powers in conflict with one another and results in more wars. Maybe this is what the greater powers wanted in the first place, but even if they did not want to get involved they kind of had to: if they did not their rivals would get stronger. In this way it is quite possible that it is the actions of the smaller states on the periphery which keep the conquests going.

This is how the second Punic war starts, for example. It is also how Caesar justifies his conquests in Gaul.

That said, at a certain point the Romans themselves were aware of the tension between the sheer power and scale of their empire, and that of the enemies they were supposedly justified in conquering. This is the speech Tacitus writes for the British chieftain "Calgacus"

You have not tasted servitude. There is no land beyond us and even the sea is no safe refuge when we are threatened by the Roman fleet....We are the last people on earth, and the last to be free: our very remoteness in a land known only to rumour has protected us up till this day. Today the furthest bounds of Britain lie open—and everything unknown is given an inflated worth. But now there is no people beyond us, nothing but tides and rocks and, more deadly than these, the Romans. It is no use trying to escape their arrogance by submission or good behaviour. They have pillaged the world: when the land has nothing left for men who ravage everything, they scour the sea. If an enemy is rich, they are greedy, if he is poor, they crave glory. Neither East nor West can sate their appetite. They are the only people on earth to covet wealth and poverty with equal craving. They plunder, they butcher, they ravish, and call it by the lying name of 'empire'. They make a desert and call it 'peace' - Tacitus, Agricola, 30

Strong stuff. But as the linked thread mentions, not necessarily what Tacitus himself believed. Still, it goes to show that at least some Romans were aware of the ambiguity of their conquests even if they then go on to conclude they were justified all along.

Further reading:

• Arthur M. Eckstein, Conceptualising Roman Imperial Expansion under the Republic: An Introduction, 2007