In my hometown Sendai, northeastern part of Japan, we usually put a fish called "haze"(gobioidei). Its face is soooo ugly but it makes the soup so tasty :)
And in eastern Japan, including my hometown and Tokyo, we use rectangle shaped mochis. But in western Japan they use circle shaped mochis.
If you live in Japan, what do you put into your zōni?
If you're not in Japan, how do you celebrate your New Year?