It used to be the case in pubs round here that the landlord would give regular customers a free tot on New Year's Day. Don't think it happens much now, though.
The owner of the one I frequent does. Mind you, she keeps it downplayed so that only we regulars get them. You have a choice between a bottle of beer or a shot (1.5oz). I'll be toddling off to meet her soonly:)
I don't know if its still done,but bartenders in the pubs I used to go to in Brooklyn always 'bought' every 4th or 5th drink...any time,not just for Christmas/New Years.