[pishpash]

This is a very nice exposition of the problem statement. However --

"Athena: You could solve the problem clumsily by requiring the mail server to ask for a password before I could use it. I prove who I am to the server by giving it my password.

Euripides: That's clumsy all right. In a system like that, every server has to know your password. If the network has one thousand users, each server has to know one thousand passwords. If you want to change your password, you have to contact all servers and notify them of the change. I take it your system isn't this stupid."

-- if this isn't a problem for you, as it isn't (or can't really be worked around) on a decentralized network like the internet, then Kerberos seems like an over-engineered marvel for a bygone era. For a closed intranet though, like universities or corporate networks, Kerberos is still around.

[icebraining]

OpenID/OAuth (incl. Google and Facebook's login buttons) are quite similar, so I don't think the approach is outdated.

[fusiongyro]

Kerberos 5 is somewhat distributed—"realms" loosely map to domains. Kerberos's architecture is very similar to Shibboleth, which is web-based and has a certain level of popularity.

[user5994461]

Shibboleth is SAML.