Using telnet you can
Connect to sites where you do not have an account, but that let you connect to use some utility, program, archive, etc. that they provide.
For example, you can use telnet to connect to the Multnomah County Library. When you use the online card catalog at the library, you use a terminal. All of the terminals are connected to the same computer. When you use telnet to connect from home or work, your computer substitutes for the library's terminal. You can look up books, check if you have overdue books, place a hold, and so on.
Connect directly to a site where you have an account.
For example, you can connect to Access's UNIX shell using NCSA Telnet. This lets you use UNIX features through an IP connection. (See the UNIX manual for information on how to use the UNIX interface.)
You can connect to any site where you have an account. For example, when my mother visits Oregon she can use my account to connect to Access (since I trust her with my account), then make a telnet connection to her account in Massachusetts. This way she can check her mail and read news on her service's computers, without having to make a long distance call.
