To a busy person, a little chime signaling the arrival of new mail amounts to nothing more than a statement of the obvious. Of course you have new mail. You always have new mail. Look in your inbox right now and you know what you'll find? New mail. You really don't need some obnoxious bell tinkling away in your system tray to tell you about it.
Message notifications, be they push or pull, do far more to break your concentration than to alert you about important new information. They ding every five minutes or so and tell you basically the same thing every time: Someone sent you e-mail. If you're very busy, and you already have enough basic awareness of your own professional life, you'll disregard the chime and keep working. If you're a little compulsive (like me), you'll feel obligated to check the inbox, breaking your focus on the task at hand to peruse the new messages. In either case, your notification has interrupted your train of thought, however briefly, to announce something that you could have guessed on your own.
The problem with notifiers isn't just that they tell you the obvious about the state of your inbox; it's that they break into your consciousness with such frequency that you could spend the majority of your day looking at (and usually deleting or archiving) two or three messages at a time without ever accomplishing any significant work. Every time you shift your focus away from a present task, you then have to spend some time refocusing on it again. If a pointless little bell draws your attention every 5 or 10 minutes, you'll be lucky to get a full hour of actual work done in an 8-hour day, and you'll never be able to establish a state of flow.
While it's nice (and usually surprising) to get an instantaneous reply to an e-mail you've sent out, the truth is that none of us expect an immediate response to our messages. Even the most wildly urgent e-mail in your inbox probably doesn't require a response in less than 30 minutes (if it did, the person probably would've called or IMed you). Most of your contacts will be satisfied if they hear from you within the same business day, and still others will happily wait until tomorrow for your reply. So why the sense of urgency to know that new mail has landed?
Some productivity mavens recommend simply reducing the frequency of your notifiers to 20 or 30 minutes, but this strikes me as pointless. Because you already know that you're going to get at least a couple of new messages in any given 5-minute period within the business day, you're better off just assuming that you pretty much always have new mail in your inbox.
Rather than allow a notifier to tell you when you've got mail, just set your own intervals for mail breaks in whatever way suits your schedule. If you're fastidious about responding quickly to important messages, check every 30 minutes. If you're more relaxed, do it once every hour or two. In my experience, getting accustomed to worrying less about the e-mail inbox is a great way to discover just how little everyone else worries about the immediacy of your replies. Sure, there's the occasional frantic weirdo who'll call you ten minutes after sending you an e-mail to ask you if you got it, but most people really don't care how long it takes you to get back to them, as long as it's within a business day, or by end of day if it's slightly more urgent.
What you gain in exchange for the relaxed mail intervals is a better shot at staying focused on the tasks that actually matter. You'll likely also find that you spend less time dealing with e-mail overall, since it takes less time to sort and archive 30 messages at once than to deal with three at a time every 10 minutes. So go ahead, turn off the notifier and try working for a week without it. You may be surprised at the focus boost you get.