Update: link-rot repaired, August 2023.
Update: added mention of a book of Conan tales by Lin Carter / de Camp, October 2018.
If you can’t afford the excellent Tantor audio books of Conan, there are now some free R.E. Howard unabridged audio stories with semi-pro and listenable narrators…
Howard’s Conan stories in free audio, ordered in story-world chronology:
* “The Frost Giant’s Daughter”
* “The Tower of the Elephant” (abridged, semi-dramatised)
* “The Tower Of The Elephant” (unabridged, narrated)
* “The God in the Bowl” (unpublished during his lifetime)
* “Rogues in the House”
* “Black Colossus” (the story text at Project Gutenberg)
* “Queen of the Black Coast” (also on YouTube)
* “Shadows in the Moonlight” (and part 2)
* “A Witch Shall Be Born”
* “Shadows in Zamboula”
* “The Slithering Shadow” (aka “Xuthal of the Dusk”)
* “The Devil in Iron”
* “The People of the Black Circle”
* “The Vale of Lost Women” (unpublished during his lifetime)
* “The Pool Of The Black One” (no longer online as free quality audio, see the full text at Project Gutenberg)
* “Red Nails”
* “The Jewels of Gwahlur” (aka “The Servants Of Bit-Yakin”)
* “Beyond the Black River”
* “The Black Stranger” (unpublished during his lifetime, aka “Treasure of Tranicos” after re-working by de Camp, to have it fit better between “Beyond the Black River” and “The Phoenix on the Sword”)
* “The Phoenix on the Sword”
* “The Scarlet Citadel” (and part 2 3 4 5 6 and 7)
* The Hour of the Dragon (aka Conan the Conqueror, a novel)
“The God in the Bowl” and “The Vale of Lost Women” — unpublished during his lifetime — don’t show Howard writing at his best. And “The Slithering Shadow” and “The Devil In Iron” are said to be far from the best of the Conan stories.
There is also a Books for the Blind audiobook of the collection of stories Conan the Swordsman (1978). This collection of briskly-plotted gap-fillers for the Conan chronology is from Nyberg / Lin Carter / de Camp. Their stories successfully mimic Howard, only lacking some of the small telling details that he carefully wove into his stories. Their book has, in the book-order:
~ “The People of the Summit” (after “Rogues in the House”) (begins at 1 hour 12 minutes into the book reading) (good)
~ “Shadows in the Dark” (after “Black Colossus”) (good)
~ “The Star of Khorala” (after “Shadows in Zamboula”) (a long story, but a lesser one – very skippable)
~ “The Gem in the Tower” (between “The People of the Black Circle” and “The Pool of the Black One”) (excellent)
~ “The Ivory Goddess” (before “Beyond the Black River”) (mediocre)
~ “Moon of Blood” (after “Beyond the Black River”) (excellent)
For those who can afford them, Tantor’s audio book collections of R.E. Howard’s original Conan and others use the modern Del Ray texts and are read with excellence:
The Coming of Conan the Cimmerian.
The Bloody Crown of Conan.
The Conquering Sword of Conan (full free-sample story).
Also from Tantor:
The Savage Tales of Solomon Kane.
Kull: Exile of Atlantis.
Bran Mak Morn: the Last King.
The Horror Stories of Robert E. Howard.
Sadly it seems Tantor can’t sell into the UK, and nor are downloads available through Audible.co.uk. So Brits will have to go to eBay and pay a premium (the days of bargains on eBay are long gone, as are the days of cheap trans-Atlantic shipping), or have an American friend buy them for you and send them over.
Also by Howard in audio…
The collection Solomon Kane: Red Shadows and three Solomon Kane poems read by a Shakespearean actor.
available. 
