I'm sure everyone has a favorite Frank Frazetta painting, the vast majority of which I'll wager depict Conan. I'll be honest and admit that I'm actually not a huge fan of Frazetta's Conan pieces, which is why my personal favorite is one I've posted here before -- his A Princess of Mars.
I'd make a very poor art critic, so I can't go on at length about the technical brilliance of this illustration and why it makes it worthy of approbation. I can only say that I like this painting, which nicely captures the essence of Burroughs's characters and stories in a way that appeals to me. In the same way that a lot of people think of Frazetta's Conan when they imagine the Cimmerian, I think of Frazetta's John Carter and Dejah Thoris when I think of these characters. No other illustration transports me to my childhood adventures on Barsoom the way this one does and that's my sole criterion for my appreciation of it.