The Chimera (a hideous amalgamation of a lion, a goat and a dragon)
Cerberus (a vicious three-headed dog that in some myths had a back covered in living serpents)
Orthrus (Cerberus's two-headed, serpent-tailed little brother), and various other creatures definitely count.
Perhaps the worst is Typhon — father of the above along with the Mother of All Monsters, Echidna — Typhon is described by some writers as being as tall as the sky itself, and having a hundred dragon-like heads, all of which screamed and breathed fire. It's not hard to see why almost all the gods had a collective Brown Note when he appeared, and fled Greece, leaving Zeus to face the creature by himself.
And then there's creatures like Scylla and, even worse, Charybdis, once beautiful women turned into eldritch things of pure horror. Scylla we at least know is horrifying to observe, looking like a giant, beautiful women from the waist up, with a scaled tail below, and the heads of six, rapid wolves snapping at her waist.
Medusa, whose face was apparently so frightening that anyone who saw her turned into stone.
Prometheus' fate of being chained to a rock and having an eagle peck out his liver each day. He endured it for hundreds of years before being released.
Similarly, the fate Cheiron the centaur faced before he sold his immortality: living forever, with the maddening poison of the Hydra eternally burning through his veins.
The fate of mortals unfortunate enough to piss off the Olympians.
Phineas, son of Poseidon, was Randomly Gifted with the ability to perceive past and future. This access to knowledge threatened the gods so Zeus struck him blind and further punished him with starvation by being attacked by Harpies every time he tried to eat.
So, you're friends with Aphrodite, and she want to marry you, eldest son of Nereus, old man of the sea. That's good, right? Well, Dad says no. You tell your girlfriend that, and even though it's not your fault, she turns you into a polyp.
Many gods of the Pantheon were terrifying in the same way as Anthony from "It's a Good Life"; by marrying incredible power to a complete lack of temperance or discipline. Even the mightiest of gods could be vain, petty, selfish, lecherous, vindictive, and very enthusiastic when it came to Disproportionate Retribution. And, unlike the deities of most other belief systems who get the same accusations from time to time, this was not a matter of Alternate Character Interpretation; according to their own believers, these gods were a bunch of cruel, vicious, spoiled children and humanity was just one of their playthings.
The few tales of cannibalism (such as Tantalus and Atreus).
Zeus makes another woman pregnant, then hides her underground. She gives birth to a giant... and dies of childbirth.
The same giant flirts with Artemis. He gets sent off to Tartarus to be forever eaten alive by eagles. This was not Prometheus, just some Casanova Wannabe.
Ephilatus and Otus tried invading Olympus. They eternally drown in the center of a waterfall, tied by snakes to a pillar, while Fate watches them as an owl. Ouch.
Some of the bandits whom Theseus defeated were known for their exceedingly barbaric cruelty such as Procrustes, who tied his victims to a bed and chopped body parts if they did not fit. Sinis was also pretty horrific: he bent down two pine trees with his great strength, tied the hands of passer-bys to the tips of the two trees, and then let go.
The Minotaur's young victims were imprisoned in the labyrinth and force to run for their lives until the beast catches and devours them or they drop dead of exhaustion, hunger and thirst. It's like the first teen slasher flick.
The future Olympians were able to live and grow in Kronos's stomach how exactly? Squick indeed.
Antaeus the giant, who was building a temple using human skulls.
The fate of the few mortals sent to Tartarus:
Ixion - bound to an ever spinning flaming wheel.
Sisyphus - forced to roll a boulder up a hill only for it to roll back down.
Tantalus - chained to a pool from which he can never drink because the water recedes. There are fruit trees whose branches he can't reach because the breeze blows them away.
The reason Ixion was there? He was invited to Olympus for dinner and started creepily and obviously flirting with Hera. To get proof, Zeus made a cloud copy of Hera and made sure Ixion could find the cloud copy easily (while hiding the real Hera). Ixion promptly attempts to rape the copy. Zeus, waiting only for the chance to catch him in the act, struck him dead and prepared the above-described punishment.
The reason Sisyphus got punished? Back then, Thanatos, the god of Death, actually knocked on your doors visibly and in person, so when he came to Sisyphus, Sisyphus knocked him out and tied him up, causing nobody on Earth to die. Ares noticed that though there was enough mangling and bloodshed going on on his favourite battlefields, nobody died, which put a bummer on the whole thing for him, so he went to look for Thanatos. After finding him under Sisyphus' bed, he freed Thanatos and the two of them killed Sisyphus then and there. In the Underworld, Sisyphus started whining to Hades about how his wife had no time for proper burial rites and how without them he could never really enter the afterlife, so Hades let him back to the world of the living to arrange things, but he told his wife not to complete the rites and stayed on as a ghost. After a while, when it was obvious Sisyphus was not planning on going back, Hades fetched him himself and put him to the task described above.
King Diomedes, who fed humans to his flesh-eating horses. In a Karmic Death and/or Ironic Death twist, he himself was fed to them.
The entirety of the Atreidae lineage (which Orestes is part of), really. They were a royal family who have been cursed by Zeus due to the arrogance of the bloodline's founding member (Tantalus, who is already mentioned above). It all goes downhill from there. Oh, yes, their story is a grim one filled with murder, incest, and cannibalism, among other things. And speaking of cursed families...
The Labdacids (AKA Oedipus' family). They received Apollo's curse from Pelops (of the aforementioned Atreidae) for causing the death of the latter's son. This curse leads them to inevitably kill each other, and then there is poor Oedipus.
Imagine marrying your own mother and unknowingly having intercourse with her! Horrible! Then, to top it all off, Oedipus gouged his own eyes out after he discovered all this.
Icarus plummets to his death after the wax keeping his man-made wings together melted from the heat of the sun.
Phaeton, son of Helios or Apollo, had a similar fate: after being allowed to drive the sun chariot, he loses control of it so bad he has to be blasted out of the sky by Zeus. His charred remains crashlanded in Italy and his sisters died of grief at the lake that formed at the crater of impact.
Athena's birth. The clanging produced when Metis forged Athena's armor gave Zeus a massive headache, and he was willing to do anything to stop the headache...ANYTHING, including go to one of his least favorite people in the world, Hephaestus, and have him split his skull wide open. Then, Athena burst out of Zeus' bleeding skull, fully grown and armored, and letting out a battle cry.
Her mother, Metis, was fated to give birth to a son more powerful than Zeus. So he turns her into a fly and swallows her whole.
After a woman seduced a king, his wife organized for the other woman's children to be killed. But the seducer switched their clothes, and the queen murdered her own kids. When the two lovers were discovered, they were tossed off a cliff and became sea gods.
Medea. Where to start? First, she killed her brother and threw his diced up corpse into the sea bit by bit to make sure she and her boytoy Jason escaped her father, the king of Colchis. When Jason dumped her for a princess, she then decided to murder the princess with a cloak that instantly turns the wearer into a fireball. She also kills Jasons' future father-in-law, and finished this up by killing the kids that the couple had together. She make her get-away by flying into the sky on a chariot driven by Dragons. Finally, Medea manages to make peace with her father afterwards by killing her uncle, who had deposed the father as king. She is Nightmare Fuel for anyone who goes through messy divorces with psychopaths.
Before she eloped with Jason, he swore a high oath never to abandon her. When he does and thus she kills his new bride to be, his new father-in-law-to-be and their children (causing Jason to be driven out of his rightful homeland upon pain of death, penniless), Hera goddess of jealous wives, women scorned and obsessed yanderes, who was Jason's patron goddess and was one of or even THE deity invoked at the oath, couldn't add any more punishment to Jason other than to let him sleep in the bed he made, ie., let him live without her giving back anything that was taken from him.
Lycaon. He (or his sons, depending on the version) knew full well that Zeus makes a habit of dropping by in disguise to see if kings and hosts behave as they should, so when the big guy did show up, they suspected he might actually be Zeus. So what do they do to put him to the test? Why, kill a child from the next village over and serve him up as food. So Zeus turns them into the first werewolves, in some versions even noting that nothing about their behaviour changed.
Expanding on that, some sources add that Lycaon had a daughter as well as sons. Her name? Kallisto- whom you might know as the woman turned first into a bear then into the constellation Ursa Major, for getting knocked up by Zeus. She gave birth to a boy called Arktos, but they got separated right after, she was wandering the wilderness and the boy went to his grandfather. The versions that mention Kallisto as Lycaon's daughter go on to also specify that the child was cooked up for a visiting Zeus being Arktos himself, who gets resurrected when Mr. Thunder realizes what happened.
Cronus eating his children one by one, with his wife powerless to do anything. (Until Gaea helps her with the hint of going to Crete and giving a rock to Cronus when she expects her sixth child...)
I'm surprised Persephone's abduction went unmentioned here. Yes, there are different versions of the myth that vary whether or not she went willingly, but in the ones where she didn't: Persephone is just out in the field picking flowers and minding her own business. She sees a narcissus that she likes and decides to pick. Except it's a trap in which Hades bursts out of the Earth and pulls Persephone into his chariot while she vainly tries to fight him off and is screaming frantically for help but no one comes because they either deliberately ignore it (like daddy Zeus in the cases where he gave Hades permission to abduct Persephone), or don't know what happened because they went down right before anybody else can intervene. The one person who does, one of Persephone's nymph friends Cyane, fails and literally cries herself into a river. Meanwhile Hades arrives in his kingdom with his bride-to-be who is scared out of her wits and drops the bomb that she is to marry him. God knows what'sgoing through the poor girl's head at that moment. Divine or not, these are terrifying circumstances to be in.