How about call the system admin? Hehe, just kidding. Do you mean how can you change the password without logging in to the console and without telnetting to the box?
In order to execute a command on the server, you have to have access to the server to execute the passwd command or to edit the /etc/passwd or shadow files manually. Without logging or telnetting in, there really isn't a way to tell the server to do what you want. You could of course use ftp to download and edit the passwd file and upload it back. You could write a custom cgi or script and execute it via the webserver but writing the script isn't trivial. You could also setup an e-mail alias that piped an email to a program that changed your password. E-mailing the alias'ed account would cause the password changer to run but again, writing the password changer isn't simple.
I think the answer to your question is no, there isn't a standard default way (at least that I with my limited knowledge am aware of) but there are a lot of ways to accomplish this with a little work.
Good luck,
GJ