Here is a list of all the Conan comics that are generally recommended to be worth reading.

Publisher:  Marvel,  Dark Horse
Publication Date:  1970-Present
Genre:  Sword & Sorcery
Creators:  Robert E. Howard

Black entries are ongoing series
Green entries are Limited series
Red entries are One-Shots
Blue is for comments

Reading List

Conan the Barbarian #1-115, 241-253 (1970)

Savage Tales #1-5 (1971)

Savage Sword of Conan #1-60 (1974)

King Conan #1-8 (1980)

Conan #1-28, 32, 39, 45-46 (2004)

Conan: Road of Kings #1-12 (2010)