Now, when I say car I mean a usable vehicle. To me, a good beater should be practical (which means no Miata), easy to repair on your own, easy to find cheap parts for, and reasonably efficient. It should hopefully be interesting as well, but that isn't necessarily a prerequisite.
The P71 fits the bill in my mind. They made roughly 400 trillion of them so parts are stupid cheap and easy to find. The 2-valve 4.6 isn't particularly powerful, but it gets out of its own way and will run virtually forever. It also returns something around 20mpg, which is just on the side of not terrible. As for it being at least somewhat interesting? Well, BOF, V8, RWD. Yes it is still kind of boring and doesn't "handle" per se, but as the last bearer of the traditional American sedan, it is at least interestingly anachronistic.