The Baku-based Azerbaijan Airlines does indeed have an "Unwanted Passengers" list. Not only does it maintain such a list, as Jason Rabinowitz points out on Twitter, but it also makes it searchable. That's right, you can search for yourself to see if your name appears on the list.
Obviously curious to see if I (somehow) made it on the list of blacklisted travelers, I entered my name and passport number on AZAL's site. Thankfully, I got a message that no information was found.
You can't just search anyone to see if they've made the "Unwanted Passenger" list — you need a passport number in order to do so. Among those who tried in the TPG office, no one is banned from flying with Azerbaijan. Hypothetically, since you get a new passport number each time yours expires, it's possible to "fall off" of Azerbaijan's blacklist once you renew your passport.
This is the only carrier we know of that has a searchable library of who it doesn't allow to fly on its metal. It's not clear what one has to do in order to get their name on the blacklist, but nonetheless, we don't recommend trying.
