[Sidnicious]

This is easy to fix.

Check the account's Advanced settings, and make sure that the account's Deleted Mailbox points at the "On the Server" trash. You may also want to confirm that the Sent and Drafts mailboxes point to their Gmail equivalents.

You can archive a message by moving it to the All Mail folder.

In iOS 4, there's an option at the top level settings of accounts created as "Gmail" accounts to archive or trash messages deleted on the device, I'm not sure how this relates to the above settings.

[ben1040]

Check the account's Advanced settings, and make sure that the account's Deleted Mailbox points at the "On the Server" trash. You may also want to confirm that the Sent and Drafts mailboxes point to their Gmail equivalents.

If you're using the Google Sync feature (to get your mail, contacts, and calendars pushed live to your device), Google presents your Gmail account as though it were an Exchange account. Consequently, iOS doesn't let you change the folder mappings like you can with an IMAP server.

[Sidnicious]

Good point.

I work around it by setting up the Google Sync account on the device without mail and adding it as an IMAP account as well.