However, I do know that when I see there is something in my inbox, I have a tendency to want to drop whatever I'm doing and see what that message is. So I've set up a system where I don't immediately see a lot of the emails that I know don't need my immediate attention. Specifically, I have multiple email addresses and I only have the inbox for one of them open all the time. I have a yahoo account that I've had forever that I use strictly for personal situations where I know I will never need to reply to the emails, like customer accounts and groupon-type stuff. I only check that once a day, while drinking my morning coffee. The second is my official university address which gets all official University communications (which never need a reply). I actually stopped using that account, as much as possible, a few years ago because it was getting so much spam but now that the school has moved to Gmail (and a spam filter that actually works), I also use it for other work-related situations where I likely won't have to reply, such as professional organizations, journal table of contents, ed policy mailing lists, etc. I check that once a day too, sometimes more if I'm procrastinating from other things. Since it is my official university address, I occasionally get emails there from people who have looked me up for some specific reason but it is really rare that those emails can't wait the 12-18 hours it usually takes for me to see them. And then there is my main gmail account that I use for almost everything else. That's the inbox that stays open all the time, and I get a pop-up notice whenever I get new mail, but since practically all of the 'form emails' I might get are routed to one of the other two accounts, a) I don't get a ton of emails coming into that address and b) when I do get a message, it's almost always something that I want to see fairly quickly.
I also have an entirely separate gmail address that I give to students. I have that account set up to automatically forward all emails to my main gmail account, and then I filter those so they bypass the inbox and go into a separate folder (but still marked unread). That way, I don't see that I have new messages in my inbox (so I don't get interrupted) but when I get other new messages (or just when I want to take a break from whatever I'm doing anyway), I'll see that there are emails in the student folder. I've found that this is a good compromise for me - I typically respond to students within, at most, a few hours, but I don't obsess about it the way I think I would if they showed up in my inbox and I got pinged every time.
I'm sure there are easier ways to do all this but this works well for me. How do you manage your email?