Anvilicious: According to this Overthinking It article the 1980s Conan movies have strong feminist, anti-racist and atheistic themes. Of course, the major screenwriter of the first film isOliver Stone, which lends some credence to that. On the flip side of that coin, though, director and co-screenwriter John Milius self-identifies as conservative/libertarian in his personal views, Conan himself is a fiercely independent warrior who eventually becomes a king on his own steam, and the film explicitly shows Conan praying to Crom (albeit in a backhanded fashion) and that there is an afterlife when Valeria briefly comes Back from the Dead.
Awesome Music: Basil Poledouris' work on this film is considered as one of the best movie soundtracks ever made. In fact, there are some music critics who consider this score to be one of the greatest classical music compositions of the 20th century.
To highlight some tracks, "Riders of Doom" is an epic anthem worthy of an army's final stand.
Complete Monster: The evilThulsaDoom starts by slaughtering Conan's village, decapitating Conan's mom while he stands next to her and selling the children as slaves just so that he can obtain weapons of fine steel from the barbarians. Later in the film, he orders a young woman to jump to her death to illustrate how much control he has over his followers before ordering Conan to be crucified. Shortly after that, we find out that he and his followers practice cannibalism. He proceeds to kill Valeria, probably Conan's greatest love in the movie-verse, with a snake arrow. After Rexor and his army's defeat in the Battle of the Mounds, Thulsa coldly tries to do the same thing to the Princess after deeming her no longer useful to him.
Memetic Mutation: Even people who haven't seen the movie can quote the "what is best in life?" scene (although the original is attributed to the real Ghengis Khan, an expy of which is in the scene).
Genius Bonus: They actually got Turko-Mongol paganism right when they had Subotai (Hyrkanian, basically the Hyborian equivalent of Mongols and Turks) proclaim that he worshiped the Everlasting Sky. In Turko-Mongol paganism, the most important god is Tengri - Lord of the Eternal Blue Sky. In fact, it's more accurate to actual pre-Islamic Turkic beliefs than the original Howard stories were, where the Hyrkanians worship Erlik, who in actual Turkic paganism, is an evil demon and the primary adversary of Tengri.
Narm: Conan's grunts of pain doesn't sound very convincing.
Narm Charm: Although many of the quieter scenes are actually well done, a good portion of the movie is narm. Awesome, glorious narm that fits both the setting and the story like a glove, somehow managing to be incredibly moving when in many other movies it would be just plain ol' Narm without any of the charm.
As Roger Ebert noted as early as the film's release: Conan becomes a Germanic superman with a black arch-enemy. (As hinted by his name, the original Conan was Celtic (or rather, his people were ancestors of the Celts) and in his original stories he had no arch-enemy at all. Also, the literary Thulsa Doom has blue eyes and straight hair and is swarthy rather than truly black; rather than seeming like an African, his race was intended to be that of a mysterious, mystical people that had vanished from the world long ago.)
Also, the literary Thoth-Amon (the other inspiration for the film's Thulsa Doom) while being non-white and wicked had several noble qualities.