Romulus and Remus
The story of Romulus and Remus is strangely similar to that of other famous mythical figures. Romulus, Remus, Perseus (slayer of Medusa), and Moses were all tossed into a river as babies: their dismal fate seemingly inevitable. None the less, all are saved by someone who finds them on the shore and they each go on to be important historical/religious figures.
It may seem surprising that these stories are so similar but it is not uncommon for cultures to "borrow" stories from other cultures; adapting them over time to suit their needs. This happens with many ancient motifs; dragons and floods are patterns that show up in ancient tales from many different mythic archetypes.
The most important story from the founding of Rome was Romulus and Remus. According to Livy (1.3-8), the story begins with King Numitor, ruler of the area to the east of Rome, who was deposed by his brother, King Amulius. Numitor's daughter, Rhea Silvia, so that she couldn't give birth to a successor, was commanded by Amulius to become a Vestal Virgin (a priestess of Rome who was sworn to chastity). This did not last for long, however, as Rhea was raped or ravished (depending on the source) by the god Mars and soon gave birth to twins.
Amulius, enraged, cast the twins into the Tiber River. Carried to safety by Tiberinus, the personification of the Tiber River, they were given to a lupa, or wolf, for care. They are soon after found by a shepherd and his wife, raised until they discover their secret identity and depose the tyrant Amulius, restoring their grandfather Numitor to kingship.
After helping to reinstate order in Numitor's city, they decide to found a new city. They go to the place where they were found on the banks of the Tiber, but a conflict arises between the brothers about which hill to found the city on. Romulus wants to found the city at the Palatine hill and Remus at the Aventine. They agree to decide by augury, or divination by birds. Remus is the first to see birds, but Romulus sees more birds. They argue, and Remus is killed in the fight. Romulus founds the city on the Palatine and names it, of course, Rome.
This coin shows the early years of Romulus and Remus. They are usually portrayed as babies and very rarely do we see an adult version of these twins.