How painful is tooth extraction without anesthetic?

Very: If the tooth still has bony attachment then it will literally be like breaking a bone slowly and tearing your gums away from the tooth. If the tooth is barely handing on, it will be very sensitive and hurt like a slow deep cut. I really don't recommend it but if you really want to good luck.

Very!: Unless it is a primary (baby) tooth which is about to come out, or a tooth severely loosened by gum disease, removal without anesthetic would be excruciating. A fine network of fibers connect tooth roots to surrounding bone. Nerves share space with those fibers and larger nerves enter each tooth. Severing those nerves and fibers is more painful than most would be willing to tolerate.