I get up to a couple hundred emails a day. Normally I don't use my phone for email, but it's nice in a pinch,
like when there's no Wi-Fi to be had. I use the stock email app from Google to manage my 7 accounts. One day fairly recently, my ZTE Android phone decided that it was going to always run the Email app in the background no matter what I did. Which means it wanted to make a sound every time an email came in, which is about every few minutes. It got aggravating quickly. My ZTE is running close to a stock version of Android, so it doesn't have all the fancy email settings in the stock app like my wife's fancy HTC smart phone.
There seemed to be no way to tell the stock email program not to play any audio notifications. The best I could do was turn off sound for the entire device.
There seemed to be no way of getting the email app not to run when I didn't want it running. Stopping the app in App Manager didn't help. Disabling it completely did the trick, but when I re-enabled it, all my accounts were gone. Not a very good solution, though it did solve the notification problem by deleting all my account info.
Really the only way I found to control the notifications is by individual account, which is better than nothing. It would be nice to have a master toggle switch for the notifications to turn them on and off in one shot, but I guess this is better than nothing.
The account settings for each account lets you control wheter a notification comes through, and whether it plays a ring tone or vibrates when a new message comes in. Setting the ring tone of each account to Silent lets me keep the notifications without the noise of it playing a ringtone every few minutes.