For some people, every e-mail is a potential emergency, and should arrive on your phone with as many jingles, vibrations, and other notifications as possible. For everyone else, cut your battery some slack, and turn of push notifications, starting with e-mail.
Push data provides immediate indications that someone has sent you an e-mail, posted on your Facebook, or tweeted a mention of you. But your phone only knows that if it's constantly, neurotically checking for new data. Turn off as many notifications as possible – under Settings, then Device, then Apps on Android, or Settings and Notifications on iOS.