The more I read about email, the more I am convinced that it will eventually go under. I do not think that we'll have to create a new system, but a paradigm shift is inevitable. Spam is unbeatable, because the only way to filter it out is by content. But every time we come up with an algorithm to detect spam, they respond with an algorithm to foil us. A classic arms race -- and nobody wins.
It was a pure fantasy, anyway, to expect that email will function just like USPS, but faster. It is about time to start using Internet the way it can be used best. The change must occur in the culture. How about whitelisting by default? May seem inconvenient at first, but once it gets a proper mindshare, it will become almost invisible. Let there be a pass of some sort which cannot be collected automatically -- for example, a subject line which you list on your website -- that can enable the incoming email to get through and to whitelist the sender at the same time. When you receive your first spam email, you just un-whitelist it and change your pass. Done.
Store your pass anywhere you want, put it out in the open if you want, just keep it two paces apart from your email listing, just enough to make it infeasible to collect email/pass pairs automatically.
If people know and expect that emails tend to be guarded with such passes, they will request you to provide them along with the email -- not much strain on communication, since passes could be as simple as your mum's name. All they need to do is to send you one "introductory" email -- and they don't have to worry about it anymore.