Can I hide the new messages notification in the Mail icon for only one of my email accounts?

Solution 1:

You can effectively turn off push notifications for a particular email account... sort of. Go to the Settings app, and hit "Mail, Contacts, Calendars". Go to "Fetch New Data", then scroll down and go to "Advanced". For the email account whose little red badges you don't want, change the setting to "Manual" instead of "Push".

This will prevent new messages from pushing a notification icon to the home screen. However, when you open the Mail app to check your other email, the app will sync the "Manual" account with the server and you'll get a badge if there are unread messages there. So, like bmike mentioned, the real way to get rid of those badges is to get closer to inbox zero.

Solution 2:

No - there's no control for that on iOS 4.3 or less. If you disable that account it will temporarily turn it off on counts but the content stays loaded on the device.

I will second the suggestion to set up a separate folder to store the majority of the unread messages and use server side filtering or a manual process to get rid of the distracting/offending messages.

My phone and sanity are both better once I bit the bullet and set up a rule that says if it's unread over a week it goes into my triage later folder. I can still search for messages using spotlight, they are all where I can find them but my phone is faster and the badge is more meaningful without that pile of messages.

I'm not quite to inbox zero, but this was a good first step for me to getting there.