Secure Shell (SSH) is probably more used these days for remote login sessions than telnet for obvious security reasons, but telnet is still widely used as a tcp troubleshooting tool. I, for example, am an output administrator so I use telnet on a regular basis and it's ability to connect to specific ports to test network connections to print devices connected directly to the network. Using ping or traceroute won't tell you if a standard Unix print hub can make tcp connections to a device (ping uses ICMP packets, and traceroute uses a combination of ICMP and UDP packets), so the most available tool for checking those tcp connections is telnet. It's a great tool for checking if certain services are "alive" on remote machines, too. For example, if you would like to check to see if the SMTP service is running on a remote machine, try this:

telnet your.isp.com 25

If the service is running, you might get something like this:

220 your.isp.com ESMTP

A simple test using telnet. It is still quite useful. Don't ever enter a password while using it, however, unless you enjoy broadcasting your passwords in plaintext to anyone on your network who's listening.