I used to go to the pub on my own to watch football a fair bit, there is a fair chance of meeting a fellow supporter giving you an instant rapport (or at least a starting point for conversation).
Occasionally if away on business I may go in a pub to eat as it is marginally less depressing than being sat on your own in a restaurant, which is pretty horrendous, especially if you order two courses and have the awkward wait in between.
I used to go clubbing on my own a fair bit about 8-10 years ago as well, was kinda weird I used to bump into people I knew (acquaintances more than friends so rarely made arrangements to meet up with them specifically). There was one place I used to attend fairly regularly because they had a good trance room and got to recognise some fellow regulars. I found it doesn't feel quite as weird as being sat in a pub because you can dance, roam around a bit, no different really from being out with a mate who has then pulled early and left you (my best mate was a bit of a player in his youth).