IPhone – Gmail in iPhone: How to delete on swipe

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

Google recommends the following configuration for Gmail on Mail.app OS X:

From the Mail menu, click Preferences > Accounts > Mailbox Behaviors

Drafts:
Store draft messages on the server > leave unchecked

Sent:
Store sent messages on the server > leave unchecked

Junk:
Store junk messages on the server > checked Delete junk messages when > Never

Trash:
Move deleted messages to the Trash mailbox > leave unchecked Store deleted messages on the server > leave unchecked

Also, trash gets emptied on its own on Gmail; mail older than 30 days gets deleted automatically, so other than particular workflows or because of lack of space on the server or locally, deleting mail already on the Trash folder should not be a preocupation.

I've seen tweaks and counter-suggestions from other reputable sources, I'm not linking them here because they are fairly old.

That said, Joe Kissell and others accuse Gmail of not following standard IMAP implementations –so much so that Mavericks accommodated its interaction with Gmail entirely to avoid duplication and other problems–, and that could be the source of many of the problems.