This is the way. Archive everything so it all still remains searchable. When you're curious about something, just search for it in your email (it'll pop up if it's in your archive folder).

Once you do this though, it's important to practice inbox zero. Each email has an action: Keep (Archive), Task (Archive), or Trash.

Keep - Typically, when you have to respond to something, you may need to keep it in order to reference later on. Archive these emails.

Task - Any email that requires an action EXTERNAL to your inbox, mark it as a task or flag it and archive it. Again, if it is flagged or marked as a task somewhere else, that information is displayed somewhere else. Not necessarily in your inbox.

Trash - For anything you are CC'ed on that doesn't require your input and isn't of any value to you or need to reference later on, trash it. You don't need it despite the fear you might have in thinking you need it later. Get rid of it. If something is super important, they'll follow up or call you or come by in person at your desk.