I'm hoping to run some sessions of AGON in the near future - a game about ancient Greek heros competing with one another to perform missions for the Gods.

Since the Haven is frequented by history/myth enthusiasts, and not by my players, I thought I'd put the question to the forum: What do the Greek Gods want?

AGON is a fairly structured game and imposes rules on the GM for scenario design. Scenarios should take the form of:
[A Greek God] needs someone to [Action] a [Person(s), Place(s), or Thing(s)]

Examples:
Hera needs someone to destroy the monstrous half-child of zeus (by another woman).
Apollo needs someone to recover the Horn of the Tritons
Hades needs someone to start a war between the people of the islands of Samos and Lesbos

What I'd really like are suggestions for cool, lesser known Greek Gods, for iconic sounding (but not over-used) monsters or mcguffins, and most of all - because this is the hardest part - a reason why the god in question wants this to be done. It's not that the gods need to justify themselves, but I think it makes for better immersion in the scenario to know the whys, and can also help to create lead-ins to future scenarios.

Any ideas would be very welcome!

A common theme is many Greek fable based stories I recall is lust. Envy. They decide to tap some mortal ass and come get them some.

Adoration. They want to be revered/adored. Mostly they make this known by wanting from you whatever you hold dearest. If you give it up, the gods know they matter more to you than anything.

I guess in retrospect 'frequented' is too strong a word.

@Serious Paul: Yes, lust is a good motivator, and I like that suggestions. I'm not entirely sure how to work it into the formula, though. 'Zeus wants someone to Retrieve a particular beauty and bring her to him' doesn't quite sound right. Zeus would just appear to a maiden in a strange form and have his way with her, not needing an intermediary. But Zeus might want someone to protect his little darling from the forces of Green-eyed Hera - that could work. I already mentioned Hera wanting the heroes to slay Zeus' illegitimate offspring.

@Doomfistmonk: Again, not sure how to work that into the formula. 'Apollo wants the heroes to give him an item they already have'. Not much of a quest there. And yet I do think there's something interesting in your suggestion - I just have to work harder at figuring out how to use it. It could be interesting to have one god have the PCs retrieve an item for him, only to have another god then come along and lay blame on the PCs for stealing it from him, and demanding they retrieve it.

Or alternatively: Zeus asks his precious followers to create a distraction so he can go on with his cheating. And it's up to the PCs to figure out how best to make Hera angry and focused on their sorry ass (or someone else's for that matter).

There are so many lesser gods and monsters in Greek mythology. It shouldn't be too hard to find some combination of them as a backdrop of your adventure. Though the problem is that Herakles killed half of the best villains, and other heroes and demi-gods claim the other half. How much freedom do you grant yourself to shape a nice mission/situation? I mean every legend has at least a couple versions, so it's not like alternative stories are taboo.

How about this one:

Bad guy: Tereus son of Ares who married Procne but desired her sister Philomela. He forces himself on Philomela and cuts her tongue. Later the mute sister reveals the truth through a tapestry to Procne, who decides to get her revenge. She serves a meal made of Itys' body (Tereus and Procne's son). At that point the gods transform them all in different birds but I think that's right where you should deviate. How about: Ares transforms Procne and Philomela in monsters (Gorgon-like stuff maybe) and they become the guardian of Tereus' palace who now lives in fear and isolation (because of a prophecy announcing that heroes are going to punish him maybe?).

Mission giver: Hephaistos who is still mad at Ares for his affair with Aphrodite. He could ask the heroes to bring him back the tapestry woven by Philomela for instance.

These are both fantastic! The first suggestion builds nicely on what Paul said and I could see turning it into a whole arc of scenarios where the PCs start off as pawns. The second is based on a nice little myth using lesser known characters with an interesting McGuffin and the potential for a good twist. The fact that it deviates from the myth is better than using the actual myth, I think. Very nice, thank you - exactly what I was looking for!

If I had a group I would love to run a Greek mythology game. Half an hour on wikipedia and I get ideas. Easy peasy

Lust and greed can be pretty interchangeable as I see it. We covet the things we see every day. Gods are often portrayed as easily slighted, and quick to avenge perceived wrongs, and quick to take what they want.