They don't work the same way they used to though. Since old school PSTN hardware is being replaced with VoIP, there is a hacky protocol called T.38 which does just enough to convince each side that it's talking to a real fax, and decodes and forwards the data over IP.
Circuit switched class five offices are still very plentiful though, and DS3-based transit networks are still nationwide. So if you want it, you can absolutely still experience phone networks without voip.
Depends where you are. In the UK, decommissioning of the PSTN has started and will be completed in the last few places by the end of next year. There will still be a "phone service" for those that want an equivalent service to their old landline, but it will be provided by a VoIP box.