Android: If you don't want to turn off all email alerts on your phone but also don't want to get pinged for every insignificant message, customise the notifications for individual labels in Gmail.
CNET points out this handy feature for setting and disabling individual alerts. To set it up, tap one of the categories or labels in the slide-out menu of the Gmail app, then press the Menu button and choose "Label settings". There you'll be able to check or uncheck the label notifications and even set a custom sound or choose vibration.
You can do this for Gmail's new inbox categories as well as your other labels so you know when you get an alert, the email is really worth reading.