I usually suggest Auld Land Syne mean "Old Times Past" although this translation suggests slightly different: http://www.worldburnsclub.com/poems/translations/auld_lang_syne.htm

Given that my good lady is from a small hamlet in Scotland (ok, Glasgow) I figure I should at least advertise the Robert Burns Birthplace museaum http://www.burnsmuseum.org.uk/ which is very good (I've been recently).

I use a "Slow Slow Quick Quick Slow" arrangement then put an some Scottish Country Dancing music because everyone is so busy giving each other New Year greetings or trying to call relatives that there's little chance of any dancing anyway.

We use New York New York to get everyone organised into a circle before 12 O'clock so we can launch into Auld Lang Syne pretty much in synchronisation with Big Ben's first Bong.