Chosen ones, fate, destiny, &c. When you get down to it, a story with these themes is one where a single person or handful of people is ontologically, cosmically better and more important than everyone else. It's eerily similar to that right-wing meme about how "most people are just NPCs" (though I disliked the trope before that meme ever took off).
Way too much importance being given to bloodlines by the narrative (note, this is different from them being given importance by characters or societies in the story).
All of the good characters are handsome and beautiful, while all of the evil characters are ugly and disfigured (with the possible exception of a femme fatale or two).
Races that are inherently, unchangeably evil down to the last individual regardless of upbringing, society, or material circumstances.
I can't stand stereotypical "dumb barbarians". "Me want to break things and drink all the ale" yeah great, man. Even Star Wars did this with the big guy in the Bad Batch (I heard it got better later but that debut episode in Clone Wars...ugh).
They can be done well but a lot of times they're written the exact same way with the same carbon copied quips.
Yeah, the difference between Conan, the extremely smart, well read, polyglot, world traveler archetypal barbarian and the "D&D Barbarians are illiterate by default" thing is pretty weird.
From what I can gather, Conan (and by extension, the whole Hyborian age) is commentary on the dichotomy between civilization and barbarism. Conan of Cimmeria is called a barbarian for all the reasons folks throughout history referred to others as barbarians (e.g. he believes that peope aren't property, that people of different faiths should interact, e.t.c.)
Also, judging by the kinds of things Conan does, he'd be a rogue in D&D terms