I agree the most with these two comments:
I don't use Conan directly and avoid mentioning the big guy. After all these years of adventuring, he really doesn't need to steal my players' spotlight.
In my campaign there is no Conan, this has the advantage that I can use the Howard stories as adventures and the players don't have to worry about a big Cimmerian tapping them on the shoulder when they feel like doing a bit of trampling the jewelled thrones!
Only one of my players has read any of Howard's tales, and he's only read a few. My campaign starts around the time when Conan was a young man, just beginning to leave his mark on the world. Here's the thing, Conan doesn't exist. His mother miscarried, and the world will never know him. This, coupled with my players unfamiliarity with the stories, leaves the world ripe for the characters to play the part of Conan. I can use Howard's tales as inspiration for my adventures, and the characters can be the great heroes of the age, playing a great role in the history of the age. I've already ran the Isle of Iron Statues (nearly exactly like the story), and my players loved it. The Isle of the Black Ones is coming soon, as well as Jordan's Conan the Invincible. I can't wait to see where this goes!
Hollywood Hogan said:
I use Conan in my campaign - every adventure. My players all take turns using him - he is by far their favourite fictional character and each and everyone of them relishes when it is their turn to role play the grim Cimmerian. It is an absolute blast - although I'm sure it would make some purists roll over in their grave.
This is an interesting idea, and I admit it has a certain appeal. Having said that, ultimately I imagine it would be more rewarding to have a character of your own creation become a legendary hero. I liken it to a great painter. What is more rewarding, copying the works of the greats that have come before you, or creating your own masterpieces? If you copy some one else's work, even if it's phenomenally done, it will still just be a copy. If you create an original piece, even if it's just good, not great, it will be more meaningful than a great copy.
But then, even with different heroes, I'm copying Howard's adventures, so take it for what it's worth!