Just a brief run-down, will go into further detail later.
Australia
In nearly all native Australian cultures the sun is feminine. Personal favorites include Gnowee, a figure in the southern cultures who wanders the earth for her lost son, and Bila, a figure specific to the Adnyamathanha, who is a murderer who roasts people over the fireplace (the true origin of sunlight).
Africa
Egyptian mythology bears the iconic Eye of Ra, a goddess that represents the physical body of the sun and the consort to Ra. Many goddesses are said to be the Eye of Ra, including Sekhmet, Isis, Wadjet, Bast, Hathor, Nekhbet, among MANY others. Most of these bear solar discs on their heads, cementing their status as solar deities. Perhaps tellingly, most solar deities in Egyptian records are goddesses, and Aten, the henotheistic/monotheistic deity of Akhenaten, had feminine traits as well.
In Dogon culture the sun is named Nay and is considered the primordial symbol of femininity, in contrast to the male moon.
Lungu/Tabwa mythology notably portrays the hyena as the de facto solar animal, having brought it into existence. While I can?t find information on the gender of the sun in their culture, the hyena is indeed perceived as female there.
Eurasia
The original proto-indo-european solar deity was most definitely feminine, and reflexes of her exist both in mythologies with actual sun goddesses as well as those with masculine solar deities.
In Celtic mythology, the predominant sun goddess can be identified as Sul/Sul, which was later adopted by the British Romans as Sulis. Her name is directly cognate with other indo-european words for ?sun?, and like the Greek Helios and Hindu Surya she is associated with the eyes. This association lead in fact to a switching of the words for ?eye? and ?sun? in Irish, with Grian being the resulting name for the sun, feminine in nature. Other Celtic goddesses speculated to have a solar role include Aine, Epona, Brigid and Olwen.
In Slavic languages, the word for ?sun? is traditionally feminine. Some Russian fairy tales depict the sun as a wife.
In Baltic mythology, Saul? is a well-attested sun goddess which was among the dominant deities in pre-christian times. Given how similar Slavic and Baltic mythologies tend to be, she might offer further insight on the ancient Slavic sun goddess.
In Norse and Germanic mythologies, the sun is well attested as a goddess; she is most well known by her Icelandic names, Sl/Sunna, but notably her Old English name, Sunne, is the origin for ?sun? itself.
The story of Rapunzel is often considered to be a relic of a western European solar myth.
In Greek mythology, Helen of Troy has been suggested to be a relic of the original Greek sun goddess. Minoan religion is assumed to have had a solar goddess as well, and many Greek goddesses are thought to be descended from this deity, and even Medusa bears solar traits like her association with the eyes. The goddess Thea (literally ?goddess?) is the mother of the Greek sun god Helios, and may be another remnant.
In Hittite mythology, the sun was the goddess Arinniti, patron of the city of Arinna. I?tanu was originally interpreted as a male solar deity, but it turned out to be another goddess.
In Hindu mythology the sun, Surya, is normally considered male, but in Buddhist cosmology Surya is occasionally female and contrasted against a male moon.
Perhaps related to the indo-european sun goddesses is the Turkic Gun Ana.
In Finno-Ugric languages most words for sun are feminine or neutral. The most notable example of surviving sun goddesses in these cultures is the Sami Beavi, hose symbol is a common shamanic motif. Hungarian mythology bears Xatel-Ekwa. Both are associated with livestock (reindeer for Beavi, horses for Xatel-Ekwa)
A solar goddess appears to have been dominant in Eastern Asia, but her worship has been gradually eroded by Buddhism and other newer religious groups. Descendants of this goddess may include the Chinese Xihe, the Korean Hae-nim and the Japanese Amaterasu.
The Ainu sun goddess is Tokapcup-kamuy, rather similar to the native american Arctic sun goddesses.
To the Basque the sun was Eki, the ?model daughter?.
In Canaanite mythology the sun was Shapash. The related pre-Islamic Arabic mythology also bears a possible sun goddess; notably, both Judaism and Islam have similar anti-solar worship statements, which may have stemmed from historical rivalry with the worship of this goddess.
Americas
Among Arctic peoples, the sun is invariably female, and has the same consistent origin story. She is known to the Inuit as Malina or Akycha.
To the Pawnee the sun was Shakaru, and notably the subject of their sun dances.
To the Cherokee the sun was Uelanuhi, and specifically stated that her warmth was coveted by men.
There is a ?Hekoolas? often listed among native American mythology lists, but I haven?t tracked her to a specific tradition.
