Rome struggled with a situation analogous to that of Athens, in which the rich not only had a virtual monopoly on political power, but in many cases had the legal right to either enslave or at least extract labor from debtors. In Rome's case, an ongoing class struggle called The Conflict of Orders took place from about 500 BCE to 360 BCE (140 years!), in which the plebeians struggled to get more political representation. In 494 BCE, the plebeians threatened to simply leave Rome, rendering it almost defenseless, and the senate responded by allowing the creation of two officials called Tribunes, men drawn from the plebeians who had the legal power to veto certain decisions made by the senate and consuls. Later, the government created a Plebeian Council to represent the needs of the plebeians, approved the right to marry between patricians and plebeians, banned debt slavery, and finally, came to the agreement that of the two consuls elected each year, one had to be a plebeian. By 287 BCE, the Plebeian Assembly could pass legislation with the weight of law as well.
Roman soldiers were citizen-soldiers, farmers who volunteered to fight for Rome in hopes of being rewarded with wealth taken from defeated enemies. An important political breakthrough happened in about 350 BCE when the Romans enacted a law that limited the amount of land that could be given to a single citizen after a victory, ensuring a more equitable distribution of land to plebeian soldiers. This was a huge incentive to serve in the Roman army, since any soldier now had the potential to become very rich if he participated in a successful campaign against Rome's enemies.
That being said, class struggle was always a factor in Roman politics. Even after the plebeians gained legal concessions, the rich always held the upper hand because wealthy plebeians would regularly join with patricians to out-vote poorer plebeians. Likewise, in the Centuriate Council, the richer classes had the legal right to out-vote the poorer classes – the equestrians and patricians often worked together against the demands of the poorer classes. Practically speaking, what this meant is that by the early third century BCE the plebeians had won meaningful legal rights, namely the right to representation and lawmaking, but those victories were often overshadowed by the fact that wealthy plebeians increasingly joined with the existing patricians to create something new: the Roman aristocracy. Most state offices did not pay salaries, so only those with substantial incomes from land (or from loot won in campaigns) could afford to serve as full-time representatives, officials, or judges - that, too, fed into the political power of the aristocracy over common citizens.
In the midst of this ongoing struggle, the Romans came up with the basis of Roman law, the system of law that, through various iterations, would become the basis for most systems of law still in use in Europe today (Britain being a notable exception). Private law governed disputes between individuals (e.g. property suits, disputes between business partners), while public law governed disputes between individuals and the government (e.g. violent crimes that were seen as a threat to the social order as a whole). In addition, the Romans established the Law of Nations to govern the territories it started to conquer in Italy; it was an early form of international law based on what were believed to be universal standards of justice.
The plebeians had been concerned that legal decisions would always favor the patricians, who had a monopoly on legal proceedings, so they insisted that the laws be written down and made publicly available. Thus, in 451 BCE, members the Roman government wrote the Twelve Tables, lists of the laws available for everyone to see, which were then posted in the Roman Forum in the center of Rome. Just as it was done in Athens a hundred years earlier, having the laws publicly available reduced the chances of corruption. In fact, according to a Roman legend, the ten men who were charged with recording the laws were sent to Athens to study the laws of Solon of Athens; this was a deliberate use or “copy” of his idea.