I think that if we discuss the sun, it's difficult to leave out the moon.
In Sumerian, Babylonian and Akkadian myths, Shamash was the child of Nannar, the moon. Shamash was the Sun-god of Justice and rode in a chariot across the sky each day. It's interesting to me that the moon would be seen as the "parent" and the sun would be the dependent. The moon was responsible for most cultures' calendars for thousands of years, until Julius Caesar forced everyone to convert from the lunar to the solar calendar before his death in 44 BCE.
In Japan, Amaterasu was the Sun-goddess and the sister of Sosanowo, the moon
In Egypt, Aten was the Sun deity forced upon the Egyptians by Akhenaten (Amenhotep IV), converting the Egyptians from a polytheistic culture to a monotheistic one, Ra was also considered a Sun God, Thoth the moon
In Greek, Helios or Apollo and Artemis
In Celtic, Lugh was the Savior/Dying God associated with the Sun, Brigit the moon
In Norse, Balder was the Savior/Dying God - Sun, and Hodur the night (possibly the moon)
As far as age is concerned, it's difficult to say who the "first" culture was to worship the sun. When nomadic tribes converted to agriculture, the sun's movements became more important, and possibly deified. I've got a date of about 10,000 - 15,000 years ago when that transition started to occur. (source - Pandora's Seed)