For a long time I thought this episode was called "Who Mourns for Adonis?", which would make some sort of sense because Adonis was also a Greek god. But no, the title is actually a reference to Adonais, a poem by Percy Bysshe Shelley, which contains the line "Who Mourns for Adonais?" verbatim (line 415). Shelley himself coined the word "Adonais", possibly alluding both to Adonis, and also to the Hebrew word Adonai, which is one of the names of God in Judaic tradition, translating loosely as "Lord". So the word "Adonais" could be read as an Anglicised plural of Adonai, with the implied meaning of "gods". "Who Mourns for Adonais?" then becomes "Who mourns for gods?" - a very apt title indeed.

That is, alas, possibly the cleverest thing about this episode.

Transcript

1
Captain's log, Stardate 3468.1. Surveying the Pollux system.
Sulu: Captain! A weird giant... hand?
Spock: An energy field, holding the ship.
Chekov: You have to hand it to it.
2
Apollo: I have withdrawn the wind from your sails.
Kirk: Give it back!
Apollo: Impudence! You need a hands-on demonstration of my might!
3
Spock: Pressure on the hull his causing ear pain in the crew. That should not be physically poss—
Kirk: All right, you win! Stop it!
Apollo: Can't handle it, huh?
4
Apollo: How like your fathers you are. Agamemnon, Hector, Odysseus. Join me on the planet.
Kirk: Get a grip. Let us go.
Apollo: Talk to the hand!
5
{the surface of the planet}
Palamas: Why am I in this landing party?
McCoy: You're the ancient history officer. And Scotty has a crush on you.
Palamas: Oooh, those are Ionic columns!
McCoy: See, that came in handy.
6
Kirk: How do you know Hector and Odysseus?
Apollo: I am Apollo!
Chekov: And I am Tsar of all the Russias!
Apollo: You take your life in your hands!
7
Apollo: {to Palamas} And you are like Aphrodite, Athena. I shall magically change your clothes.
Scotty: Keep your hands off her!
8
Apollo: Worship me, as your ancestors did!
Kirk: No!
Apollo: So, you show your hand. How sharper than a serpent's tooth it is to have a thankless child!
9
Apollo: You will worship me! Give me an offering. Your ship.
Kirk: What does a god need with a starship?
Kirk: Aha! Now I have the upper hand!
10
McCoy: How can we beat Apollo? If we raise a hand against him, he'll lightning bolt us.
Kirk: Godlike alien who flirts with a female crew member and cuts us off from the Enterprise... It's unlike any situation we've ever been in before.
11
Spock: Captain, Spock here. We punched through the hand. I'm going to destroy Apollo's power source with phaser banks. Stand back!
Apollo: Noooo!!
12
Apollo: The time of gods has passed. They bite the hand that feeds them...
SFX: Fade {Apollo fades away}
Kirk: Well, we won that one, hands down.