A hackerspace, or "makerspace", is a private organization comprised of members who share a shared workspace and, generally, the interest of building things.
Chances are there's one near you. Members normally pay a monthly fee, but most have "Open Make Nights" where you can pop in and use the equipment without needing a membership. You can find your local hackerspace using this tool, which lists over 2,000 hackerspaces.
In an effort to remain a relevant community resource, many public libraries now have 3D printers available for use! Find your local library and call the information desk to ask if they have any 3D printers available.
If you're a student, your university can likely provide you with access to one. Call your university library's information desk and they can direct you to the college/department that will give you access.
Many 3D printing businesses and professionals advertise their printing services on Craigslist. Most charge you when you pick up the model. Be sure to ask for references or photos of their work.
If cost is the primary reason you don't have a 3D printer, you may not know how low prices have gotten. In the last few years, 3D printers have come way down in price. I picked up my Creality Ender 3 for $179 on GearBest. I also wrote a full Ender 3 review if you want to check it out!
A 3D-printed house? What about a store that 3D prints you a custom shoe? And will we be able to, one day, 3D print our way to Mars? It's all possible!