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So I've noticed a trend in different myths across the world of the sun being represented by a male diety and the moon being represented by a female diety:
Apollo and Artemis from Greek myth
Ao and Po from Hawaiian myth
the God and Goddess of Wicca
And the two are usually lovers or siblings.

But today I was flipping through my book on Japanese mythology and remembered that it was the exception.
In Japanese mythology, Amaterasu is the sun goddess and her brother, Tsukuyomi is the moon god.

My question is this:
Why do you think it is common for the sun to be represented by a god and the moon by a goddess?
Why is the opposite true for Japanese myth?
Why, for that matter, does Amaterasu have more power and authority considering that she is a woman and not the first born of Izanagi and Izanami?
Do any other cultures that represent the sun and moon with deities represent the sun with a woman and the moon with a man or stray from the sun-male moon-female pattern?

Good question.

I know of many goddesses who are associated with the sun, or some aspect of the sun, but I am not sure that there are that many male gods who are associated with the moon...

Sun Goddesses
Aditi - a Hindu Goddess from India, keeper of the light that illuminates all life and ensures consciousness. She gave birth to the universe and the heavenly bodies.
Aine - Irish Goddess who represented the spark of life. Her festival was celebrated on Midsummer’s eve. Later she was remembered in Christian times as the fairy queen

Akycha - An Alaskan solar Goddess who once lived on earth as a beautiful woman. She fled into the sky after her brother raped her.

Amaterasu - Japanese Shinto Goddess, her name means great shinning heaven. She is the head of the Japanese pantheon and her emblem, the rising sun, appears on the Japanese flag.

Bast - The Lion Goddess of sunset, among her many roles she symbolized the fertilizing rays of the sun.

Beiwe - Sámi Goddess of Lapland, she was celebrated at the summer solstice for providing the light the plants needed to grow. These in turn fed the reindeer that were vital source of food, clothing and tools for the people.

Bila – The cannibal Aboriginal Goddess who provided light for the world by cooking her victims over a giant flame. She was chased away but the world was then plunged into darkness, so Bila was captured and tethered to the earth.

Brigid - A Celtic fire Goddess, as a solar deity her attributes are light, inspiration and all skills associated with fire.

Chup-Kamui - A modest Japanese moon Goddess. She traded places with the sun God as she was so embarrassed by the adulterous and lecherous behavior that was occurring at night.

Djanggawul Sisters – Aboriginal Goddesses from Arhemland. These daughters of the sun gave birth to all the plants and animals. Their magical power objects were stolen from them by their brothers.

Hathor - Egyptian Goddess of the sky. Hathor is depicted with the solar disk indicating that this is one of her many areas of influence.

Hekoolas - Native American Goddess, with the help of the trickster Coyote, man was able to convince her to light up this world.

Medusa - The Greek Goddess is said to derive from an earlier Anatolian deity. This theory is supported by images of her with a lion that symbolized the power of the sun.

Pattini - A Sri Lankan solar deity who represents the heat of the sun's rays.

Olwen - Welsh sun Goddess, her name means “golden wheel.”

Saule – Lithuanian, golden haired Goddess. She rode across the sky in a chariot pulled by two white horses with golden manes, battling with the powers of darkness.

Sekhmet -A Lion headed Goddess of Egypt, she represented the destructive qualities of the suns rays causing drought and famine.

Shapash - Phoenician Goddess whose name meant “torch or light of the Gods". In addition to being a solar Goddess she was also able to travel through the realms of the dead.

Solntse - Slavic sun Goddess

Sunna - Nordic Goddess of the Sun, also known as Sol, her chariot was pulled across the sky by two horses

Uelanuhi - Cherokee Goddess of the Sun, her name meant "apportioner", as she was responsible for dividing time into units. Her warmth was captured for man by Grandmother Spiderwoman's web.

Walo - Aboriginal Goddess who traveled across the sky with her daughter, Bar. One day Walo realized that the reason the earth was parched was due to their combined heat, she then sent her daughter back to the east so that the earth could become fertile and bloom.

Wuriupranili - Another Aboriginal sun deity who lit a bark torch and carried the flame through the sky from east to west. At the western sea, she dipped it in the water, then used the embers to guide her under the earth to reach her starting point again.

Wurusemu - Ancient Hittite sun Goddess. She is also known as Arinna.

Xatel-Ekwa - Hungarian Goddess, like many other ancient European solar Goddesses she is linked with horses as she rode through the air on her three steeds.

Moon Gods

Arma - Hittite lunar personification whom some think is connected with the Greek god Hermes.

Khons/Khonsu - Egyptian Moon God
Amen's consort was Mut. Together they had a son, Khons or Khonsu the moon god. His name means "the wanderer." He may have been believed to be capable of flying.
Other Egyptian moon gods:
Thoth
Osiris
Min
Duau

Mên - Phrygian lunar god also connected with fertility, healing, and punishment. Characteristically, Men is depicted with the points of crescent moons on his shoulders. He wears a Phrygian cap. Mên carries a pine cone or patera in his outstretched right hand and rests his left upon a sword or lance.

Sin/Nanna - Sumerian Moon god.

Soma - Hindu Moon God

Yarikh - Ugarit Moon God
Yarikh or Yarih was the lover of Nikkal -- a Sumerian sun goddess.

there is also Nanna (also known as Sin) in Sumerian mythology. he is the Moon God, and the chief deity of the Gods. the Sun God, Shammath, is said to be jealous, aways hungering for the power of the Moon, stealing the Moon-Given magic and enchantments from any object or creature touched by the Sun's Rays.