This is an excellent question. However, it is difficult to answer, because Rome lasted for over one thousand years. In light of this, there were many times when Rome waxed and waned. Moreover, there were times when Roman went through radical transformation. For example, Rome went through three major constitutional shifts - kingship, republic, and empire. In light of this, I will assume that you are talking about the empire.
The Romans chiefly did three things to remain in power.
First, under the emperor Diocletian, Roman divide the empire into two halves under four leaders. This was called the time of the tetrarchy. This was a very important development, because Rome had to govern such a vast empire.
Second, when there were great economic problems, such as inflation due to debt and the debasing of their currency (sounds a lot like today), Diocletian passed a price edit, where he tried to stem inflation.
Finally, the Romans always sought to make their army as strong as possible. This was a constant in their history.
There where many, but they all failed. The first was persecuting the Christians. Second, was getting rid of the germanic tribes mainly the visiogoths, celts, and huns. There where instances that the barbarians starved the roman cities from within. The barbarians weren't potentially dumb. There where signs of cannibalism even during this time. The romans also tried to create allies as well this worked due to unite the system. They created a military government as well to maintain force if people rebelled. think of it as ancient marshal law. They also tried to conquer Israel and succeeded expelling the Jews from there homeland which I deem as evil in a sense, but as Nero came to power he lit his own city on fire and blamed it on the Christians. It wasn't the fault of Christians that started the Dark Ages it was a mixture of several things that lead to it. Many of the Roman stopped caring about the people so the people rebelled. second, the destroying of libraries and the destruction of schools lead to it as well. Third, Disease was a huge factor during this period and cleanliness was the fault. fourth, the merchant system became destroyed as trade with the outside world fell. Fifth, the rise of barbarism & conquest became a huge benefactor as places where tooken over again again and again. sixth, The rise of slavery began during this period as immigration became widely a trend. Last, People started losing knowledge slowly, and people became unable to read and write.