I just set my Gmail account to:
1) Filter from:...@gmail.com to Skip the Inbox (Archive)
2) Forward to .Mac
And then on the iPhone I set up my .Mac settings for incoming mail (mail.mac.com/username/password) and Gmail settings for outgoing mail (smtp.gmail.com/username@gmail.com/password).
This allows me to check my email using the .Mac website or Mail, but still keep a copy on Gmail's server if I need to go back and see. I did this with .Mac because Gmail doesn't have IMAP. I'd rather have everything synced up (i.e., I delete an email on the iPhone and it's also deleted on the webmail/Mail.app on my computer).
All of your sent items are saved on Gmail's website, though. You don't see the sent items reappear as new mail in your Inbox on the iPhone either, since they skip the inbox on Gmail's side.