While you would get very slow speeds, I don't see why you could use a modem to make a point to point dial-up connection. You could definitely do it in older versions of Windows (like NT 4 "old"), and I know that with some work, you can make Linux treat it as IP over serial (ironically, generally requiring the use of a serial modem, too). The cost would likely be fairly high, just to try it out, unless you have several of Linux-supported business-class modems hanging around (like the old black/red USR ones, or rack units from office modem banks that are being discarded, these days).
I wouldn't want to, since even crappy DSL is many times faster, but it is an idea that hasn't been mentioned, yet 🙂.