I'm yet to hear of any culture that uses any base other than ten, for one simple reason - we have ten fingers. People began counting on their fingers.
Quod Erat Demonstrandum
To be reasonably exact, the vernal equinox year is currently about 365.242375 days long. Other measurements using other references can be found
here.
The Gregorian calendar provides for a year of 365.2425. Thus we have leap years every four, not including century years not divisible by 400. Thus 1700, 1800 and 1900 would not have been leap years but 2000 was.
The difference between these year lengths means that, in theory, the calendar will be one day behind in 8000 years. But then the vernal equinox year is constantly changing so that can be ignored for the moment.
EDIT: Now that is interesting; according to
Wikipedia the Yuki used a base-8 system because they used the space between the numbers to count, the Mayans used base-20 because they used their fingers and toes and the Sumerians used base-60 for various practicle uses like counting time and measuring angles. Not sure if they used it for counting though.