In 'Rogues in the House': While the house's Evil Genius is about to activate a trap on one of Conan's buddies, Conan 'grabs the nearest bar stool and throws it, cracking the villain's skull open'. He then makes a remark and goes back to his drinking
Another one in 'Rogues in the House' is the manner in how Conan is ultimately caught by the guards. He flees from them while drunk, and runs into the door frame so hard, he knocks himself out! (This is our Boring Invincible Hero?)
"Did I tell the Stygian to fall in love with me? After all, she was only human!"
In Black Colossus, Princess Yasmela decides to put Conan in charge of her army. She summons the nobles to her, gives a speech about how she's chosen who will lead her armies, and pulls back a curtain:
It was perhaps not an entirely happy moment for the disclosure. Conan was sprawled in his chair, his feet propped on the ebony table, busily engaged in gnawing a beef-bone which he gripped firmly at both hands. He glanced casually at the astounded nobles...
The ending of "The Scarlet Citadel", where Conan, after an epic adventure of imprisonment, encounters with monsters, escape, and winning his kingdom back from a usurper witnesses his ally Pelias' magical revenge on Tsotha-Lanti and essentially reacts with I Need a Freaking Drink.
Possibly an unintentional one, but in "Queen of the Black Coast", Conan realises that he's standing under a black lotus and is being drugged by its scent. What does he do? Go away? Hold his breath? No, he attacks the flower with his sword.
In one of the later Savage Sword of Conan stories, Conan's pirate crew has been captured and taken prisoner at a port city in Kush. When taken to the royal court, he notices the queen "giving him the eye." Conan is later tossed in a cell with the demon Imhotep, a former ally who has been enchanted to resemble a human. He remarks to the demon when the guards appear outside that they have likely arrived to take Conan to the queen's chambers, and if he manages to escape, he "may" come back to free the demon. It then turns out that the guards are there for Imhotep, who is the queen's lover. As Imhotep is being escorted out, he turns to Conan and tells Conan not to worry, "as I may come back for you."