I'm interested in creating a website that will have a city name as a prepended word for each city it is launched in, like craigslist.com does. Is that possible to do without buying a new domain for each one? Would that be common across any domain registrar?
Creating subdomains has nothing to do with the registrar, it depends on your hosting company.
Some will allow unlimited subdomains but may limit how many sites you can have. This isn't a problem if you only have one site that they all point too and you parse the subdomain.
Some hosts restrict how many subdomains you can have.
You will need to do research based on your idea, don't forget to allow for growth in case you are successful and need to expand.