Occasionally there was a list on the chalk board, first and last name, of everyone who owed a tab. This was at late as 2008. This was also in a city of like 150; so not even a small town.
Heh, my bar is like this. Been going there long enough that I get to run a tab for a few weeks before the owner finally (jokingly) gives me a hard time about it.
A bowling league I was on for example would allow you to run a tab of drinks/food and pay at the end of the night as they know you are not going to dine and dash.
Granted that was a combination of a bar/bowling alley, but a few other bars that I used to frequent in my younger years after seeing you as a regular would also have no problems letting you run up a tab.
I have never been to a bar on my first visit that had full trust in the patrons right out of the gate, but then again I only was in that scene for 2-3 years.
And this isn't just because I'm a regular. I've seen it happen plenty with people from out of town too. The only thing they'll take your ID for is their mules so you don't run off with a copper mug.