Depends on the auth mechanisms in use, the simplest ones are still still pretty straightforward. Nowadays you just use the TLS equivalent of telnet (openssl s_client).

POP3:

  1. run openssl s_client -connect myserver.example.com:995
  2. enter two commands: "user myusername" "pass mypassword"
  3. profit

SMTP & AUTH PLAIN is only slightly more complicated but similarly just an additional protocol command, connecting with s_client. (You need to generate the auth string in another shell window with: echo -ne "\0username\0password"|openssl base64)