In Roman mythology, Sol was the god of the sun, equivalent to Helios in Greek mythology. See Helios for more details.
In Norse mythology, Sol (also Sunna, Sunne and Frau Sunne -- derivation of the words sun and Sunday) was the goddess of the sun (called Alfrodull meaning "glory of elves"), a daughter of Mundilfari and Glaur, and wife of Glen. Every day, she rode through the sky on her chariot, pulled by two horses named Alsvid and Arvak. She was chased during the day by Skoll, a wolf that wanted to devour her. Solar eclipses signified Skoll had almost caught up to her. It is fated that Skoll will eventually catch Sol and eat her; though she would be replaced by her daughter.
The earth was protected fom the full heat of the sun by Svalin, who stood between the earth and Sol. In Norse belief, the sun did not give light; this was caused by the manes of Alsvid and Arvak.