This is one of the core narratives of Rome.
The story as told by Livy 
After the expulsion of the king the Tarquins obtained the support of Lars Porsena, the Etruscan king of Clusium, who marched towards Rome with his army.
The city of Rome was well defended by a wall and by the Tiber, but the Sublician bridge would have offered Porsena's army a passage into the city had it not been for Horatius Cocles. Cocles was on guard at the bridge with his men when he saw Porsena's army suddenly take the Janiculum hill. Cocles' men began to run away, but he called them back, telling them that there would be no safety in the city if Porsena's army could enter. He told them to tear down the bridge while he and two others, Spurius Larcius and Titus Herminius, held the invading army back. These three stopped the enemy's charge in the narrow approach to the bridge and held them off while the bridge was being destroyed. When the bridge was nearly down, Cocles sent Larcius and Herminius back and faced the invaders alone.
Cocles challenged the Etruscan noblemen to single combat, but for a while there was nobody who would accept the challenge. Then, the army threw their spears at Cocles who caught them on his shield and refused to give ground. Finally, the remains of the bridge crashed into the Tiber. Cocles prayed "Holy Father Tiberinus, I ask you to receive these arms and this soldier, in your favouring stream." He jumped into the river in full armor and against all odds and in spite of the enemy weapons reached the safety of the riverbank.
A statue of Cocles was erected in the comitium, and as much land was given to him as he could plow around in one day.
The story in later literature
- Matthew B. Roller, "Exemplarity in Roman Culture: The Cases of Horatius Cocles and Cloelia". Classical Philology, volume 99 (2004), pages 1–56