"Amra! It is Amra! The Lion has returned!"

Conan bounded out on the bridge and stood poised above the upturned black faces, ax lifted, black mane blown in the wind.

"Who am I?" he yelled. "Look, you dogs! Look, Ajonga, Yasunga, Laranga! Who am I?"

And from the waist rose a shout that swelled to a mighty roar:

"Amra! It is Amra! The Lion has returned!"

The sailors who caught and understood the burden of that awesome shout paled and shrank back, staring in sudden fear at the wild figure on the bridge. Was this in truth that bloodthirsty ogre of the southern seas who had so mysteriously vanished years ago, but who still lived in gory legends? The blacks were frothing crazy now, shaking and tearing at their chains and shrieking the name of Amra like an invocation. Kushites who had never seen Conan before took up the yell. The slaves in the pen under the after-cabin began to batter at the walls, shrieking like the damned.

Demetrio, hitching himself along the deck on one hand and his knees, livid with the agony of his dislocated arm, screamed: "In and kill him, dogs, before the slaves break loose!"

Fired to desperation by that word, the most dread to all galley men, the sailors charged on to the bridge from both ends. But with a lion-like bound Conan left the bridge and hit like a cat on his feet on the runway between the benches.

"Death to the masters!" he thundered, and his ax rose and fell crashingly full on a shackle-chain, severing it like matchwood. In an instant a shrieking slave was free, splintering his oar for a bludgeon. Men were racing frantically along the bridge above, and all hell and bedlam broke loose on the Venturer. Conan's ax rose and fell without pause, and with every stroke a frothing, screaming black giant broke free, mad with hate and the fury of freedom and vengeance.

This quoted from The Hour of The Dragon by Robert E. Howard. This passage take place after Conan has met with Publio, a merchant from the old days when Conan was widely known as Amra.

As a result of a quarrel with a superior officer, Conan left Turan. After an unsuccessful try at treasure-hunting in Zamora and a brief visit to his Cimmerian homeland, he embarked upon the career of a mercenary soldier in the Hyborian kingdoms. Circumstances - violent as usual - made him a pirate along the coasts of Kush, with a crew of black corsairs and the Shemitish she-pirate Belit as his partner. The natives called him Amra, the Lion.

After Belit was slain, Conan became a chief among the black tribes. Then he served as a condottiere in Shem and among the southernmost Hyborian kingdoms. Later still, Conan appeared as a leader of the kozaki, a horde of outlaws who roamed the steppes between the Hyborian lands and Turan. He was captain of a pirate craft on the great inland Sea of Vilayet and a chief among the nomadic Zuagirs of the southeastern deserts.

He led a band of Kozaks, raiders on the Steppes, they marauded, they stole, pillaged and burned at their leisure. He also served in the Turanian army, amongst others, leading forces against foes, he demanded the respect from the men, killed those who stood in the way. He bedded women, betrothed or single, slew beasts and men as one, without hesitation. He was an outlaw that had absolutely no respect for law or civilized justice, at least not until he was in a position of authority.

There was an instance in "The God of the Bowl" where Conan was hired to go into a museum and steal a diamond goblet. He was caught and questioned, but he refused to give up the name of the man who had hired him.
Later, when that man enters the story, Conan still makes no attempt to identify the man that hired him for the break in. It was only after the man refused to admit that he hired Conan, and offers him up to the guard for punishment, that Conan goes on a rampage and starts killing people.
He kept his word and expected the person who hired him to keep his.

Another instance comes from "Vale of Lost Women". Conan tries to coerce a female captive of a Kushite chieftain into having sex with him. He offers to free her and kill her brother's murderer. She actually made the initial offer and Conan laughed at her, stating that her Kushite chieftain captor would give her to Conan upon request. Then he makes the offer to her. At the end of the story, Conan holds true to his part of the bargain by betraying and murdering the chief. Conan frees the woman from her end of the bargain stating that he has never forced a woman against her will. In "The Frost Giants Daughter" however, he nearly forced Atali to his will. He crushed her against him, only to have the snowed earth rush up to meet him. Had he been able to hold on a bit longer, he may just have forced Atali against her will, although it is up for debate as to whether she had Conan under some sort of spell.

In "Beyond Black River" Conan the Cimmerian saved the colonists from the Picts. The interesting part of that scenario is that Conan didn't save the colonists because he loved them, he did it mostly because he hated the Picts.

Conan's honor stemmed from his belief in his own word, right or wrong. Once he had given his word, he went above and beyond the normal means of honoring it. Conan, from the mountains of Cimmeria was just as big an enigma as any in Hyboria. He commanded his life, his and no other. Conan was impulsive, his emotions swayed his decisions. He was a slave to none, a master to all. So, yes, he does know honor, just not the civilized version of deceit and dishonor. Robert E. Howard called it a "Rough Code of Honor" or "Barbaric Chivalry".