Kanban is an agile methodology uniquely suited to the way I do email.

Kanban is a very simple agile project management methodology. Basically, your team keeps track of outstanding atomic tasks in a prioritized list. As you get done with a task, you turn it in for testing and pull the next highest priority task off of the queue. This is the basic setup. The team lead is in charge of prioritizing tasks. You can add in things like difficulty estimation if you need to track and predict team work output. Generally, you will also have daily standups of 5-10 minutes in order to synchronize the team, and provide for some element of serendipity (you're having trouble with ? I can help you with that).

Most of my emails are read-only. They don't represent tasks to accomplish, but some do (reply to Grandma, friend someone on LinkedIn, schedule an outing). When I can't do a task right away, I leave the email unread so that my email client sorts the tasks to the top. From there, I either do them or they stay unread forever with me going back every once in a while to be disappointed in my lack of initiative. If I could treat task emails as tasks - and get all the advantages of task tracking along with that - I suspect I would be more productive at accomplishing them (though I may be underestimating the power of my own laziness).

Enter KanbanMail, a rather genius idea that just popped up on HackerNews a couple days ago. It sets you up to treat task emails as tasks, rather than emails. You can track the status of each of your outstanding emails. To be clear, I have not tried it - it's in closed beta right now - but I am watching this closely. There is one downside, which is the price: the developer wants to charge $12/mo (edit: this is now incorrect; please read the below edit) for it. I don't think I'd get that kind of utility from this tool. If I were of the mind to spend money on email, I would first pick up a privacy-respecting email service (something like ProtonMail - though their proposed ICO turns me off a bit). It does remain a clever idea though, and I'm curious to see what sorts of related tools will pop up.

Edit 2018-10-17: The developer, Ethan (@booligoosh on Disqus, and I'd bet other places too) contacted me via Disqus and mentioned he'd changed his pricing. I think the new price makes it a lot more tempting; being just under $10/mo as opposed to just over is probably worth a lot psychologically. I've run into a lot fewer issues with my read/unread system, so I don't feel pressure to switch at the moment. I'll let you all know if/when I give it a try.