There are lots of monsters in Conan stories:
There's a Rhemorraz mentioned by name (possibly the origin of the beast as far as I know) in The Lair of the Ice Worm.
There's a giant slug in the Hall of the Dead.
There's a giant skeleton in the Thing in the Crypt.
Frost Giants in the Frost Giant's Daughter, though that was a dream (OR WAS IT? DUHT-DUHT-DAHHHHH!!).
A Giant Snake guardian in The Devil in Iron.
Then there are the strange Lovecraftian beasties like:
The medusoid man-serpent in the God in the Bowl.
The amoeboid cloud-thing in the Curse of the Monolith.
The demon from beyond in the Vale of the Lost Women.
The winged demon thing and the were-hyenas in the Queen of the Black Coast.
The demon in the Snout in the Dark.
The strange many-limbed abomination in the Castle of Terror.
Thak the ape-man in Rogues in the House.
The animated gold statue in the Blood-stained God.
The winged demons in the Hand of Nergal.
The elephant-headed alien Yag in the Tower of the ELephant.
And many more!
And those are just in the first two collections of short stories and re-writes.
The thing that sets Conan monsters apart from D&D monsters is that in Conan there are typically only one of a monster, ever. In D&D, you've got lots of Griffons, lots of dragons, lots of mermaids, lots of lizard men, losts of orcs, goblins, umber hulks, ropers, rust monsters, what-have-you. Dragon magazine publishes "ecologies" of how these monsters fit into the real world as if they were naturally occuring species.
Conan, like Mythology, treats monsters as MONSTERS. They're abberations, strange, mysterious. They don't have ecologies because they're MYSTERIOUS! No one knows anything about them, how they got there, or what they're doing there, generally. If they're naturally occuring, they're the last of their species and dying out, the remnants of a lost world. Otherwise, they're imported for far-away Lemuria or Mu or some place exotic. The trick is to make them unique, scary, and mysterious. Did I mention mysterious enough?