What email protocol or server supports the use of message labels or tags in place of using folders for organization?

Email protocols have nothing to do with the organization of the email.

The idea of labels or tags in email was a concept introduced by GMail. To my knowledge no other email server or client has them implemented. RoundCube is an oft cited web based mail client for IMAP and POP email servers (the current standards for accessing received email of which GMail also uses). There is an open RoundCube issue for labels or tags. You may wish to subscribe to that. I believe it's the closest you'll get to tags or labels outside of GMail currently. Postfix, Dovecot, and Roundcube are typically used together for a full featured self hosted email server.

hmmm. Thanks sag47. That lead me to search around a bit and find mention of IMAP keywords, which sound like they can be used like labels or tags.

For instance, there is a feature request for K9 Mail: https://code.google.com/p/k9mail/issues/detail?id=4101

It mentions a plugin for Roundcube to use IMAP keywords, which are already used in Thunderbird.

I think I found my mail client: https://www.mailpile.is/

Note sure yet how they implement Labels, but I suspect it is through IMAP keywords.

That's cool, nice find .