I set up an account at emailkarma.com (sadly, taken, by Xobni, no less!) as a recipient. I set a default free karma amount (say, 100) for new senders, a default karma amount for unsigned emails (say, 50), and route all my email through the service. I also set up a whitelist of known good senders with an infinite karma balance.
People who email me for the first time will automatically be issued 100 karma points by the system. They have one of two options:
1. People who don't know about the karma system can email me directly, but their emails will "spend" the default amount for unsigned emails. When their balance reaches zero, their emails get de-emphasized.
2. People who know about the karma system can choose to spend their remaining balance with me by tagging the email subject with [karma: pointvalue]. Unimportant emails can be assigned less value, and if they absolutely need to email me, then they can spend more of their karma.
Incoming emails are sorted by date and by karma spend. I can reward relevance by giving them more points to spend, and/or by setting their default karma spend to a higher value. I can punish stupidity by adjusting karma accordingly. Webmail interface, or a thunderbird plugin, maybe?
Senders can view their karma balance for a given recipient and default spend (both uneditable) by emailing the service to prove identity and signing up.
Arrington, for instance, can reward good tipsters with more karma, and punish PR trolls by slapping them with a karma penalty.
You could apply this to other forms of communication, too-- your facebook/friendfeed, twitter, etc., though those would have to be passive (relevance weighted by karma balance, no discrete spend available per post/recipient).