Mythology
The exotic Spock is compared several times to mythological gods by fearful humans and aliens. Since TOS incorporates many significant literary and classical themes into its stories, these claims are worth investigating. How closely does the equally iconic Spock resemble Vulcan, Pan, and Lucifer? We'll look into each figure to find out.
Vulcan. Vulcan is the ancient Roman god of the flame and the forge. His Greek equivalent is the Olympian God Hephaestus, for whom there are many elaborate stories. The first human visitors to Spock's planet might have bestowed the name, in reference to its dry, smoldering climate. The people of this planet are called Vulcans, though Spock says he is "Vulcanian" in an early episode. It's speculated that the planet has a different name in its native language, just as many of Earth's nations do today.
There are a few characteristics shared between the god and the people, like Spock. In some myths Hera, queen of the gods, gives birth to Hephaestus on her own; in Amok Time and The Search for Spock, we see that Vulcan is ruled by matriarchs. We know that before their mastery of logic, this race was ruled by passion. So Vulcan, god of destructive fire, and his unfaithful wife Venus, goddess of love and beauty (or lust and vanity), are fitting symbols of these ancient times. Most Vulcan rituals that continue in the 23rd century would strike humans as pagan. (Vulcan had his own festival on August 23, Vulcanalia.)
Still, we can't say Spock bears much resemblance to Vulcan himself. The god is disfigured and ugly; Spock is physically superior to humans and, we might say, reasonably attractive. Vulcan quietly broods; Spock is either cool and confident or totally angst-ridden. The god's servitude - crafting all metal and magical items for the other Olympians - would point to a similarity in rank. However, while Spock is under Kirk's command, many are under his, so our first officer has more authority and diverse responsibilities than the old blacksmith.
When Spock is called Vulcan, it refers only to his place of origin, and its environment. " Hot as Vulcan" as Dr. McCoy would have it.
Pan. In Who Mourns For Adonais?, Apollo says Spock looks like Pan. The Vulcan is properly annoyed at this, since he surely takes insult at being likened to a frivolous satyr. Apollo might only mean that he has pointed ears, but the god alludes to more than he realizes.
Pan's domain is the opposite of Vulcan's. Fields and valleys, rivers and mountains: wherever there is fertility and spring, he'll be. But since ancient times he has also been associated with decadence. His race, the satyrs - horned half-men, half goats - are attendants to Dionysus, the god of the vine. In contrast to the Apollo, god of light, rationality, and order (who Spock apparently meets!), Dionysus represents murky depths, fluidity, and entropy. Spock oscillates between these polarities.
But returning to Pan, we find that in spite of his carefree demeanor, he had trouble at home and in relationships. His mother spurned him for being imperfect at his birth, as Sarek does Spock according to The Final Frontier. His efforts to whoo nymphs all ended badly, as do our Vulcan's affairs. Our word "panic" is derived from a sensation said to be cased by Pan, of loneliness that strikes in secluded spaces. Spock is clearly a lonely guy too.
There remain some points of contention. Spock plays a lyre, like Apollo, and not the pipes like Pan. His isn't given to frolicking (unless struck by spores) and has a lot of "issues" a god might shrug off. But Apollo's words are not ridiculous as they first seem, though Spock is probably embarrassed to admit his affinity with a passionate creature.
Lucifer. Lest we should think TOS is confined to pagan times, some Christian mythology is presented in The Omega Glory. The native Yangs believe Spock to literally be the devil, based on his appearance and lack of heartbeat. (The Vulcan heart is lower.) McCoy also teases him about his demonic looks, most memorably in The Apple.
The name "Lucifer" originally referred to Venus, the morning star. It's found in the Old Testament book Isaiah, but came to be equated with Satan in St. Jerome's translation. The New Testament contains a few references. Yet the archetypical figure of Lucifer was established not in the Bible but in John Milton's Paradise Lost of 1667. Within, he is a sympathetic figure, a prideful archangel who is cast out of heaven after waging war on God. He then becomes the serpent who tempts Eve in the Garden of Eden. He is commonly depicted as having pointed ears and slanted brows (like Spock) but also wings, horns, and possibly a goat's legs. (Taken from the classical satyr.) Sometimes he is instead rendered as a beautiful androgyne (angels are sexless), as William Blake has done (see image). Though Spock if definitely masculine, he is slim and seems to wear eye make-up, sometimes blush.
Kirk more often plays this "devil" role than Spock, forcing native populations out of their happy but unproductive states and (probably) into misery. This comparison is made explicit in several episodes. Spock is his captain's accomplice, as Mammon and Beelzebub were to Lucifer in Milton's text, but our Vulcan usually doesn't agree with Kirk's reasoning.
If Spock does not have much in common with the devil himself, but is he evil? I would say not - he's too nice most of the time, and does good work for Starfleet throughout the galaxy. But unlike Kirk, he's not inherently a "good guy." Spock has done some questionable things, and we understand that he constantly fights the impulse to do others.
While ancient myths inform Spock, he doesn't represent a single quality or ideal as the ancient gods do. Rather, he is a modern character: conflicted, flawed, but with the capacity for change. He is a symbol of literal thinking and composure, but he embodies much that we can relate to, and so becomes mythic.