The Punic Wars
The most influential wars in Roman history has to be the series of Punic wars fought against the people of Carthage. The first Punic war was set on the backdrop of Sicily and its smaller surrounding islands. Rome, after conquering the Italian mainland, sought to take the nearby islands, Sicily included. They were beaten to the punch though, by a group of pirate mercenaries who began attacking the city of Messina. When Messina's ruler asked for assistance from both Rome and Carthage, the trouble began. Both Rome and Carthage arrived at nearly the same time and began to fight each other. This was the beginning. Rome had an advantage with its Naval forces and strategic superiority, and once Rome had taken over the sea, Carthage had no choice but to give up.
Carthage didn't give up completely though. They began to colonize Spain to open new trade opportunities. These colonies did run well for a while. But in 218 BCE a section of the Carthage army attacked and took over the Roman town called Sagunto. This began the Second Punic War. This is the most famous Punic war because it has one of the most creative and oddest military maneuvers of all time. This was Hannibal's march over the Alps with elephants and a large force of soldiers. This was a gutsy move and many perished in transit, but it was worth it for Hannibal. Hannibal attacked a force of 15,000 Romans (over 2 legions!) and almost completely destroyed them. Hannibal did not press forward though. A Roman legion was ordered to follow but not engage Hannibal. This prevented Hannibal from setting up a base camp and stopped him from building a defensible fort. Later Hannibal did small jumps forward, but didn't directly attack Rome. Instead he tried to wrest Rome's allies from their side. Meanwhile another Carthage army was moving in from Spain and Rome was in serious jeopardy. If the two armies had joined together, it could have made a force that could have taken Rome. The armies didn't join, and Roman legions were able to crush the Spanish Armies and intimidate Hannibal from attacking. In fact, Hannibal was pulled out and ordered back to Carthage in 203. An Army led by Scipio was able to purge Carthage from Spain and by 206 BCE Spain was a Roman territory. Scipio then traveled to Africa and met Hannibal's forces head-on. Roman discipline won over Hannibal and a was a huge victory for Rome. With a large Roman force breathing down their collective necks, the people of Carthage pleaded for a treaty. It was granted and everything in the Mediterranean went to Rome.
The last of the Punic wars was less glorious. Carthage had been beaten badly in the second and never recovered its military powers, but it was quickly becoming an economic force. Carthage became a threat to Roman merchants, so through a heavy barrage of lobbying the Senate was convinced that Carthage must be destroyed. So in 149 BCE Roman forces attacked straight on from the harbors and with little difficulty decimated Carthage. The buildings were scrapped and burned and the area claimed for the Empire.