Is there a Chinese equivalent song of 'auld lang syne'?
In fact, this famous song has a Chinese version called 《友谊地久天长》(the friendship will last forever), however, we traditionally don't sing songs to celebrate over festivals, so this song is not popular in this peroid of time.

I can't think of such a popular song as "auld lang syne" in the west. Over this period, you wll find a lot of songs(different melodies, different lyrics, different singers) with the same theme "happy new year" on the street or in the markets(to convey the happiness or to attract more customers). I would like to recommend Timi Zhuo(卓依婷), a female singer famous for her "new year" type songs.