Ancient Rome's territorial growth only began after the expulsion of the last Etruscan king, Tarquinius Superbus, in 509 BC. Tarquin campaigned against Rome all the way up to 496 BC, after which he died a year later. These battles, fought against Rome's Etruscan neighbors, also gave rise to the stories of Roman heroes, who exemplified the virtues of the Republic, such as Horatius Cocles, who defended the Pons Sublicius bridge across the Tiber from invading soldiers of the Etruscan Lars Porsenna, and Mucius Scaevola, who defied the king after he was captured.

Rome then completed the conquest of the Etruscans over the years; however this was only a small part of Italy as a whole.

Afterwards, Rome was sacked by the Gauls under Brennus in 387 BC, and this allowed the militant Romans to form alliances with other Italian tribes, who, after recovering and warding off the Gauls, Rome would later conquer.

One especially competent enemy were the Samnites, who took more than 60 years to conquer. Rome eventually defeated a coalition of many Italian groups, which confirmed the Roman Republic's place as the dominant Italian power. If the Kings had not been expelled, Rome might have just been another Latin city-state. So pretty much, Rome's early expansion was due to the Etruscan threat.

"Roman Empire" by Nigel Rodgers provides lots of in-depth information, including the Roman state's early years.