Since the first answer talks about some of the causes, I will go into some of the results.
First, I will assume that you mean civil wars - - Marius vs. Sulla; Caesar vs. Pompey; Octavian/Agrippa vs. Antony/Cleopatra. If we go into greater detail, there were even more. One observation is that many of these civil wars happened during the end of the republic (even if they did not know it was the end of the republic). From this perspective, something had to be done to restore peace and stability. This paved the way for Octavian to come into power. One can even make an argument that it was these wars, in part, that made room for Octavian. That said, he ushered in the peace of Rome (pax romana). The people loved this peace and quite frankly needed it. The bloody civil wars ravaged the Roman people. A quick glance at Vergil's work show the ethos of civil war and the hope for peace.
Eventually, Octavian (later to be called Augustus) introduced a new form of government - the empire. After Augustus, there would be emperors. Also from a cultural point of view, Augustus' reign would produce some of the most important works in the Latin language - Vergil, Horace and Ovid, to name a few. However, it must also be stated that civil wars would continue. In 69 AD, there was no less than four rival emperors fighting it out.
It's probably important to first note that there were several civil wars throughout Roman history. This particular one is often referred to as Caesar's Civil War. Ceasar, Pompey and Crassus, all through different avenues, formed the first triumverute. When their terms expired, Pompey remained as the sole consul. In the ensuing time, Caesar became a very powerful and popular military leader; so powerful, that Pompey became nervous and ordered JC's army to be disbanded. Caesar said he would if Pompey broke up his own army. Pompey did not, which first led to important figures such as Marc Antony declaring loyalty to Caesar, and eventually led to Caesar crossing the Rubicon River and declaring war on Pompey. Caesar, of course, won this battle but was eventually assassinated by the conspirators. Long story made short, as a result of Caesar's defeat of Pompey and the chaos that ensued after his assassination, the Roman Republic started an extremely quick decline. This ended in Caesar's officially named heir, Octavious, being named the first emperor of Rome; thus, the end of the Republic and the beginning of the empire.