Horny Vikings: The Cimmerians are presented as warriors searching for Valhalla as heard in this exchange with Subotai:
Crom is strong! When I die, I must go before him and he will ask me: what is the riddle of steel? If I cannot answer he cast me out of Valhalla and laugh at me! That is Crom! He who is strong in the mountains!
Katanas Are Just Better: Played with. Yamakazi Kiyoshi, the sword-master for Conan The Barbarian, explicitly trained the cast in kenjutsu with Katanas; and in fact Conan does practice with a Shirazaya (wooden handled) Katana early in the film. However, due to the bulk of Schwarzenegger's arm muscles, he was unable to perform the more elegant moves that Gerry Lopez (Subotai) and Sandahl Bergman (Valeria) were able to use throughout the movie, making him look clumsy and uncoordinated in comparison in spite of Conan supposedly being the best swordsman of the trio.
Misery Builds Character: The movie even opens with the Nietzsche quote "That which does not kill us only makes us stronger."
Multi-Melee Master: His experiences as a gladiator have made him this, especially once he goes to train with the weapon masters in the East. Some of the weapons he fights with early on are fairly rare and exotic.
Nemean Skinning: When Conan finally finds the Atlantean Sword inside the tomb, the wolves that had been hounding him wake up, waiting for him. Cut to Conan wearing their skins.
The Stoic: At Valeria's funeral pyre, Subotai poignantly pointed out: "He is Conan, Cimmerian. He Will Not Cry, so I Cry for Him."
Warrior Poet: Conan is a literate warrior. And there are these pieces of dialogue from the director's cut:
Conan: I remember days like this when my father took me to the forest and we ate wild blueberries. More than 20 years ago. I was just a boy of four or five. The leaves were so dark and green then. The grass smelled sweet with the spring wind. Almost 20 years of pitiless cumber! No rest, no sleep like other men. And yet the spring wind blows, Subotai. Have you ever felt such a wind?
Subotai: They blow where I live too. In the north of every man's heart.
Conan: It's never too late, Subotai.
Subotai: No. It would only lead me back here another day. In even worse company.
Conan: For us, there is no spring. Just the wind that smells fresh before the storm.
Faux Affably Evil: Doom almost seems regretful when he notes that all Conan has done with the passion his people's massacre has devoted him is to plot revenge and then get caught...and then orders him crucified within the same breath.
Karmic Death: Perishes by the very thing he searched in the first place when he devastated Conan's village, the thing he treated with disdain afterwards : the steel, Conan's father's sword.
Might Makes Right: His philosophy of "Strong Flesh, Weak Steel" (which the trope doesn't actually describe) is essentially this - what use are weapons against the (physical or mystical) strength of the individual if it's sufficiently powerful to make the world conform to it?
Scaled Up: During the orgy scene, Thulsa Doom transforms into a giant snake and exits through a hole in the wall. In the film it's unclear why he did this, but in the novelization it explains that Doom could sense the presence of Conan and his allies, and realizing the danger he was in he transformed into a snake as a way of making a quick exit.
Scary Black Man: Somewhat of an aversion. Thulsa Doom has black skin, but he also has blue eyes and straight hair. According to the director's commentary they wanted Thulsa Doom to look like he was a member of a race that has since vanished from the Earth.
Doom: Infidel defilers. They shall all drown in lakes of blood. Now they will know why they are afraid of the dark. Now they learn why they fear the night.
Trick Arrow: Fires snake-arrows — arrows that are originally snakes, are pulled out and magically made into arrows, then fired, then they turn back into snakes. This is too awesome and scary to be laughed at - it ends up doing in Valeria.
Fluffy Tamer: Took care of Thulsa Doom's giant snake before Conan killed it.
Horny Vikings: His name is evocative of the Norse mythology and his look is very similar to Viking-themed Heavy Metal bands like Manowar. Given that Sven Ole-Thorsen is Danish, this was probably intentional.