Mashable's Alex Perry wrote just the other day that one should never bother to clean out your email inbox. Sort of right, sort of wrong. Me, I'd go crazy if I left 250,000 email messages in my email inbox. His point, though, is that you might as well save everything forever in email, and have it available to search through as needed. That's something I completely agree with. But he misses the point-- you don't have to "leave it in the inbox" to do that. In Gmail, for example, just "archive" it all at some point, and it is still there for you, in "All Mail," and available to be searched, without specifically cluttering up your inbox. So keep all that mail, but empty the inbox out periodically.
My inbox is my to-do list. I review what's in there, I get done what I need to get done, and I tag or archive (or both) everything else. When I went on vacation last week, I created a "WIP" (work in progress) label, and moved everything that needed follow up over there. Everything else I just archived, after making sure I didn't need to take action on any of it. That way I had a clean inbox, reviewed what I needed to review, and then set aside things into a special place if they needed later action.
But you don't even need to be that fancy. In Gmail, just archive everything you're done looking at. That way you can both keep your inbox clear of clutter, and still save everything for future searches.
If you REALLY want to get fancy, start setting up labels, which some folks might call tags or filters or folders. They're quite handy.