Alas, I am no Zeus. Therefore, creating a character for me takes good old fashioned mortal, mental and mythological elbow grease.
Mythology provided archetypes of characters for millennia before Joseph Campbell came along. The Alpha Male, the Nurturing Female, the Brooding Loner, the Kick-Ass Chick -- there's nothing new under the sun.
But myths don't only provide the characters, they can also provide some framework for a story - ways to develop your characters into something more than archetypes. How many ways has Hades been transformed into the Beast who steals Persephone/Beauty from the love and light of her family? In the hands of a skilled storyteller, he's more than a distant immortal, an ideal from far away. He's a man in unending, soul-searing agony until he sees the one being who can give him surcease from his pain and loneliness.
Sometimes, the myths are half-told. They give us a hint of a character or of a story and it's up to us to flesh out those few drops of inspiration. For instance, there are three Gorgons, but we only ever hear of Medusa. In fact, she wasn't even a proper Gorgon - she was a mortal woman cursed into that form by Athena. So what about the other two? Stheno and Euryale? What's their story?
When you're using an archetypal character, it helps to be able to see as big a picture of that character as possible. To go back to Medusa, it wasn't enough to simply see her as a monster with snakes on her head. I needed to know the myth inside and out. That's how I discovered that she was created by Athena for fooling around with Poseidon in Athena's temple. But that still wasn't enough, so I went back to the Gorgons. Why make her a Gorgon? They were protectors, meant to inspire terror in the enemies of the Olympians. In fact, Zeus put the aspect of the Gorgon on his shield, using the image of a power older than Classical Greece to reinforce his own power.
Older than Greek? Okay. I looked up ancient snake goddesses and snake symbolism. Ladon the serpent protected the golden apples of the Hesperides. Blood taken from Medusa's right side was made into a healing potion by Aesclepius. A snake is wound into a symbol of healing in the Rod of Aesclepius. Moses formed a copper snake and twined it around a pole to heal the Israelites. Snakes were regarded as wise and cunning and could even gift people with second sight. Wisdom? Healing? Protection? The worship of a chthonic (earth-based) serpent deity had as many positive notes as it did negative.
So when you look to archetypes and ancient tales to build a story, be sure to cast your net wide. You'll pull in more than you dreamed!