my iphone constantly notifies me of new email even when i'm not in the email app. Some people might find this useful but when i'm at work i check my email anyway so it's annoying when the phone vibrates through out the day!
Go into settings and make sure that "Fetch New Data" is set to off, then make sure "push" is off and Fetch set to "manual". scroll down to "Advanced" and for each of your mail accounts select "manual"
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iPhone, the Swiss Army knife of the 21st Century.