You can still get dialup telephone modems, they are really expensive considering what you can get a consumer router for now days.
I would think almost any modern application will be almost unusable on a 56k maximum connection. It will work I guess if you wait long enough and things do not time out.
They still are used by companies to get remote access to a router when the internet or private line fails. This lets you reconfigure a router without sending someone to the site. The tend to be hooked to console ports that are simple line mode command screens that are simple enough to tolerate the slow speed.