Do you know what "Auld Lang Syne" means?
Lets be honest, it's sort of weird to sing a song that sounds like it's telling you to forget old friends. This year, I found myself on the Auld Lang Syne wikipedia page looking for an answer. It turns out, the song is based on an old Scottish song and "should old acquaintances be forgotten" is meant as a rhetorical question.
"Auld lang syne" literally translates to "old long since", meaning long long ago.
So it turns our Harry & Sally, in their twisty Nora Ephron wording of it, have it right. Remember old friends and memories as you toast the new year tonight!