The Mayan Calendar
The Mayan Calendar was very accurate for such an ancient civilization. The Maya could predict when the sun would set, what time of day it was, and even when there would be an eclipse. They ended up being only 4 days off from our current time. They even predicted the world would end in 2012 sometime in December. The Mayans could, using their calendar predict when the days would be shortest, longest and so on. They could also use this calendar to know when eclipses and such had happened hundreds of years ago. Most interesting is that they did this without computers.
Mayan Home Page