Yes. You'd be surprised at how many systems are still connected to modems. Three that I know of.

1) Certain agencies in the government only all data to be passed to them by dial-up. The stance is, it's more secure than sending it over the internet.

2) System managers that have monitoring systems set up to send pages via dial up fail backs.

(https://encrypted.google.com/search?hl=en&q=sending+sms+over+dial+up)

3) systems that have to send faxes, may not be set up to ignore incoming phone calls.

*edit: Adding 1 more I know of.

4) Telco's providing turnkey solutions, maintaining the circuits and the routers, still use dial up for out of band access.

I've either seen or have been told about all 4 of those in the last two years.

Never heard of it.

*Thanks chris.