How to change the Mail “Archive” folder for email account/s

This can now be accomplished very easily in iOS 7.

(n.b. The following assumes that you have already setup your account on the iOS device. These steps described are for a generic IMAP account. Also, when ALL CAPS are used below, it is to reflect how Apple has it listed in iOS 7.)

1. Launch the 'Settings' app on your iOS device
2. Scroll down and then tap on "Mail, Contacts, Calendars"
3. Tap on the email account you want to configure.
4. Tap on the 'Account' line with the > at the top of the next screen
5. On the 'IMAP ACCOUNT INFORMATION' screen, scroll all the way down until you see 'Advanced' and tap on it
6. Now you will see a 'MAILBOX BEHAVIORS' screen, showing you which mailboxes are used for Drafts, Sent, Deleted, and Archive mailboxes.
7. Important: Tap on the 'Archive Mailbox' line and verify that you have chosen the correct folder on the server where you want messages to be saved.
8. Once you have verified that the Archive Mailbox points to where you want it to go, look for the 'MOVE DISCARDED MESSAGES INTO' section, and tap 'Archive Mailbox' (instead of 'Deleted Mailbox')
9. Important: These changes will not be saved until you properly exit the configuration screen. To do this, tap the '< Account button near the top of the 'Advanced' screen.
10. When you get back to the 'Account' screen, tap 'Done' at the top-right corner.

If you'd like a step-by-step guide with screenshots, I have created one and made it available at: http://share.luo.ma/TUAW/guides/Archive-Email-Instead-of-Deleting.pdf

In the GMAIL settings, it says show or not the All Mail folder in IMAP:

So, it is your choice to show the All Mail folder on your computer or not.

There is nothing to break by choosing which folders will show on your computer from mama google's web email.

The All Mail folder is a feature of the Gmail, not your email program. So if you do not want to see it locally then disable it. Also All mail is just a bucket where a duplicate from all other folders reside for easy search. It is not real folder, just a collection of emails from other folders.