Hmm. I think Conan is less of the model for D&D than Fafhrd & the Grey Mouser are -- I remember being shocked at how much those books felt like D&D when I first read them -- but Conan, thanks to the comics and movies, is vastly better known.
The elaborate thieves guild, the petty wizard rivals (who are definitely quadratic in nature), the ramshackle and corrupt-but-lovable city with a whole underworld full of adventuring opportunities below them, and the now obligatory temple quarter full of dozens (or hundreds) of gods -- that's all from the Lankhmar books.
In contrast, I have a harder time drawing a line between Conan and anything in D&D. He's not the model for the barbarian (as has been said, he's a fighter/thief, as is Fafhrd). The magic level is far lower. The priests don't match how clerics behave or function in most games. I don't think there's even any monsters* that make the jump, beyond the general idea of snake people, but even then, the Yuan-Ti function a lot more like something from the Lovecraftian mythos.
* Maybe Howard's take on frost giants, but that's debatable.