When Conan got smashed and bumped into a camel, and then just turns around and knocks it out with one punch to the face.
When Conan meets the Wolf Witch, he learns that she has information about the Children of Doom, but that "there is a price." Cut to the next scene, where Conan is on top of the Wolf Witch screwing her brains out. Somehow, I don't think that Conan took much convincing. This scene is even funnier if you've got the director's commentary on, as Arnold dryly comments "Conan scores a lot in this movie."
Immediately after an epic montage of Conan and his gang becoming legendary outlaws, Conan passes out drunk into his oatmeal.
After he passes out, King Osiric's guards show up and Valeria nudges him to try and rouse him and get up only to shove him to the floor, seeing she's getting no hope from him she clumsily reaches to her sword.
Thulsa Doom asks why Conan hates him so much, to which Conan gives a passionate speech about how Doom destroyed his village. Doom replies with a bone-dry "Ah," with James Earl Jones perfectly communicating in just one syllable "Yeah, you kind of have a point there."
During his gladiator days, Conan is given a lady to, ahem, spend some time with. Not only is he surprisingly gentle with her, but once he lays her down, he surveys her with his hands on his hips and look on his face as if he's thinking, "Okay...now, what do I do with this?"
Conan and Subotai discuss their religious beliefs.
Conan: What gods do you pray to?
Subotai: I pray to the Four Winds. And you?
Conan: To Crom. But I seldom pray to him; he never listens.
Subotai:*chuckles* What good is he, then? It's like I've always said...
Conan: Crom is strong! If I die I will have to go before him, and he will ask me "What is the Riddle of Steel?" And if I do not answer he will laugh at me and cast me out of Valhalla. That's Crom, strong on his mountain!
Subotai: Ah, my god is greater.
Conan: Crom laughs at your Four Winds. Laughs from his mountain.
Subotai: My god is stronger. He is the everlasting sky! Your god lives beneath him.
*Conan gives Subotai a skeptical look. Subotai laughs*
Note that Conan's father had already told Conan that Crom lives in the earth, as opposed to the gods of the sky. So as far as Conan's concerned, Subotai's jest that "your god lives beneath mine, therefore he's inferior" doesn't hold much water.
From the scene where Conan, Valeria, and Subotai raid Doom's palace, Conan fights both Rexor and Thorgrim; a mis-timed hammer strike from Thorgrim ends up knocking over one of the pillars. Thorgrim looks at his hammer, then the pillar with an expression like, "Damn...did I do that?"
Akiro the Wizard. Straddles the boundary between eccentric and insane beautifully.
Conan's ridiculously nonchalant and somewhat half-assed attempt to infiltrate Doom's cult. Especially when, in a ploy to nab a priests garb, he gets the man on his own by claiming that he is "afraid and shy".
Conan's prayer to Crom is between Awesome and 'The Most Backhanded Prayer Ever':
Grant me revenge! And if you do not listen, then to hell with you!
Valeria briefly attempts to convince King Osric that Subotai died fleeing the tower... seconds before he's led in by guards. The king gets a chuckle out of it.
Conan and Subotai question a merchant about the Cult of Set, and he nonchalantly notes that "two, three years ago, it was just another snake cult." Snake cults apparently are a dime a dozen in the Hyborean Age.