I tend to be a pen and paper kind of person since I just like to be able to pick up one file folder (a real one, not a computer one) and actually see the message without having to boot anything up. What I do is have one file for each customer, and when they email about a detail that I need I print it out and put it in their file. Then I delete the email.
When I get emails from other businesses regarding advertising, receipts, etc., I print them out or respond to them, then I delete the email.
If I have something long-term that I need to deal with (key codes for software, website registrations) I'll make a folder in my email and put the information there. Then I delete the email.
If someone has sent me something that I don't really need to reply to but I think I might need the email in the future, I re-send it to myself to make it searchable in the "sent" emails, then I delete the email.
Are you sensing a pattern? I use my email so much, and so much information goes through it, there's no way that I'd be able to keep up with everything unless I keep a pretty blank slate. Too many things in the inbox and you start to forget to respond to people, things get buried, and soon you're two weeks behind in answering a client's question.
An empty inbox can make you act faster on things instead of leaving them until "later", whenever that happens to be. If you only have one email sitting staring at you it doesn't feel as overwhelming as having that one plus a bunch of other old ones that make it look like you have a lot more work to do than you actually do.
Some people make a folder for each client and move their emails into those. Like I said, I prefer to have a hard copy, so I print things out. Whichever works best for you, do it, then delete the email.
When you check your email do it at a time when you can actually respond to them as well. Don't just peek to see what's there right before you have to leave to go do something else. The reason things pile up is that we look at them and think "I don't have time for this now, I'll deal with it later." Then we forget and the email just sits there. Deal with things as they come up, but make sure that you have time to deal with them before you get into your email to begin with.
An empty inbox will make you feel so much more efficient, and a lot less frazzled. It really will.
Kara Buntin owns A Cake To Remember LLC, online cake supplies at www.acaketoremember.com and www.acaketoremember.etsy.com