I'm sure most of you reading this blog (at least those of you in/from/having lived in North America) have been to a Chinese restaurant and seen the paper place mat with the Chinese Zodiac animals on them.
Taken from this website.
Of course, one thing many don't know is that the 5 Chinese Elements also affect your animal sign (wood, water, fire, earth, metal), as well as Yin and Yang, the month, and double-hour of your birth.
Another interesting (and slightly annoying for me) thing that's still in use here in Korea [don't know if it's still being used in China or not] is that back in the mostly illiterate, agrarian times, lower class people usually didn't record their birthdays.
To calculate how old you are, you are born 1 year old, and every New Year you get one year older. Instead of counting years completed on your birth day like in the West, Chinese count the number of calendar years in in which you've been alive.
So for me, being born in December, the two months or so before Chinese New Year count as 1 year, so Koreans always try to tell me I'm two years older than I really am.
And to tie this into RPGs, using systems like this (as is or modified) can be a good way to make your fantasy world's calendar a little different. Also, the animals could be totem animals of barbarians or humanoids, immortals/deities, 'noble animals' (like in LotR or Narnia) or Animal Lords, etc.
You can also switch things around. For example, in Vietnam, the Rabbit is replaced by the Cat (so this year will be the Year of the Cat in Vietnam, the Year of the Rabbit in China/Korea/Japan).