A cursory net search revealed that apparently the Mayans had four or five separate calendars, none of which actually chronicled 365-day cycles. Like pretty much every other civilized culture, they knew the sidereal year has 365 + days but they didn't explicitly encode this in their system; they just did the calculation in their heads, I guess. I admit the sites I looked at don't have that much in the way of credentials, though.
Quite a few cultures, especially around the Mediterranean where they used base 60 a lot, had 360-day years. The Romans used such a calendar for around 400 years. They just reset it whenever the seasons got seriously out of whack. The farmers had their own methods of judging the seasons anyway, so it wasn't too important what the official season was.
--SiliconDream =PN=