I've read Howard's Conan, cover to cover, and I'm here to tell you they are great stories, and while an older, non-dead Howard might have eventually felt some embarrassment over some of his works, the man has never written anything I would consider shameful. He was a stark writer on stark subjects.
Oh, and on the misogyny thing... by the standards of his time, Howard was a radical egalitarian who championed women's intellectual and moral equality. In "People of the Black Circle," we meet a noblewoman who is fully Conan's co-protagonist in the story.
Those were mostly later writers who tried to soften the edge. Howard's original stories generally portrayed non-caucasians as wicked, sub-human, amoral or all three. Love the material to death, but the racism and misogyny is there in spades. As others said, you read it through a filter.
Conan obviously inspired the Barbarian class.
I somewhat disagree. Caucasians *are* the evil guys in several stories. They tend to be decadent, greedy, prone to betray, and tend to fiddle with magic and social "costumes" that make them not honest. Conan (that is, cimmerians) quite very much is the opposite of that. They are ruthless, bad mannered and savage, but they are "safe" from the "civilization decadence" and have some kind of personal honor code. Several savages share this traits, regardless of colour (such as kushites), and several white guys are complete pricks
Conan inspired the 1e Unearthed Arcana Barbarian, but the 4e 'Primal' Barbarian seems closely modelled on Slaine, the Warped Warrior from the 2000AD comic. The 4e designers have stated that Conan was the model for the 4e Fighter class, AIR.