I'm not very good at explaining archetypes, since I don't completely understand them myself. Here's the dictionary definition of archetype:
archetype: "the original pattern or model of which all things of the same type are representations or copies; an inherited idea or mode of thought in the psychology of Carl G. Jung that is derived from the experience of the race and is present in the unconscious of the individual"
Here's the notes TB gave me describing Mr. Jung's archetypes.

The Wise Old Man Archetypes
There are 4 main male archetype figures that fall under the Wise Old Man archetypes category. For each figure, there is a negative corresponding figure. They are as follows:

The Father : The Ogre
The Prince : The Wanderer
The Warrior : The Dictator
The Priest : The Black Magician

The Father
The Father is the authority figure representing law and order. He is very masculine, a provider and a protector. He is often depicted as the King in literature.
The Ogre
The Ogre is the oppressive and cruel father who threatens his children with rigid discipline and severe, often fatal punishment.

The Prince
The Prince is the youth and the seeker. He is the hero and literally the prince in literature. It is he who must take the archetypical journey.
The Wanderer
The Wanderer is only slightly different from the Prince. He shuns the commitment and responsibility of the journey; therefore, he does not realize his full potential and cannot become the prince until he does so. He is the evil but often gorgeous or charming villain in literature.

The Warrior
The Warrior is bold and daring. He is successful, ambitious, strong, brave, and relentless. Often the prince and the warrior are one in the same.
The Dictator
The Dictator, on the other hand, is aggressive and blinded by his own ambition and ego. His emotions are severely repressed and neglected.

The Priest
The Priest is wise and knowledgeable and able to commune with the gods and spirits.
The Black Magician
The Black Magician at first appears to use his power for good, but is revealed to be evil and a trickster.

The Great Mother Archetypes
There are 4 main Female Archetypical Figures that fall under the category of The Great Mother Archetype. As with the male figures, each female figure has a corresponding negative side. They are as follows:

The Mother : The Terrible Mother
The Princess : The Fatal Siren
The Amazon : The Huntress
The Priestess : The Witch

The Mother
The Mother is protective and maternal, she loves and nurtures her children.
The Terrible Mother
The Terrible Mother wants to possess and smother, devour and destroy. She is angry and jealous, enslaving her husband, lovers, and children.

The Princess
The Princess is an eternally youthful child-woman and a flirt. She has the power to attract people and people are attracted to her.
The Fatal Siren
The Fatal Siren is the bad girl. She is not at all interested in marriage, home, or family. She has quite another agenda; she is a home wreaker, every man's erotic fantasy. Her mission is to steal the Prince away from the Princess.

The Amazon
The Amazon is the successful career woman who is perfectly able to compete with men.
The Huntress
The Huntress may be successful in her career but this is do to the fact that she hounds and despises men.

The Priestess
The Priestess is filled with intuition and instinct. She can speak to and interpret the will of the gods and spirits. She interprets signs and omens; she is at peace within herself.
The Witch
The Witch (or Sorceress) is in touch with the gods or spirits, but she is trapped in her own world using her power for evil. She appears in dreams and symbolizes the negative aspects of womanhood.

Akio is compaired to the Prince's bad side; the Wanderer:
Dios' duty as the Prince was to save all the Princess' in the world. When he allowed Anthy to stop him from completing his duty as the Prince, he failed his mission and became the Wanderer. As an adult, Akio tries to use Anthy to help him to complete his journey, which can only be done by taking the people's Swords of Hate (which I assume were created for the Prince when he failed in saving the Princesses). Akio makes Anthy believe that it is her duty to take these Swords, therefore ignoring his duty as the Prince.

Anthy is compaired to the Witch and the Fatal Siren:
Anthy is often called a "witch" towards the end of the series. I don't quite know if those who call her that are refering to the archetypical Witch, or they just call her that... heh... anyways, Anthy is the Witch in that she holds Dios' sword within herself and sealed away Dios' power. She is compaired to the Fatal Siren because she is quite alluring to all of the Student Council. She is also very protective of of Akio and would've liked to keep him away from Utena.

Utena is compaired to the Princess and the Prince:
Even though Utena repeatedly calls herself a Prince, she is not able to become one*; only because she is female. When Akio begins to seduce Utena, he often calls her a princess and she even becomes like one... too bad she is actually in love with the Wanderer...
* in RGU girls are unable to fulfill a Prince's role. In other series and stories though, females can fulfil a Prince's role. (just think of Sailor Moon always saving Tuxedo Mask's pansy ass ^_~)