If your app uses OAuth as a means of authentication, you are likely storing users' OAuth tokens in a database. To maintain the secrecy of these tokens, you can use encryption both in transit and at rest. This article shows how SecureDB can encrypt OAuth tokens in a matter of minutes.
Additional third party integration with Gmail has been possible (you only have to look at all the contact import features from sites like Facebook), but these have either been clunky manual procedures that involve exporting contacts to a CVS file, or they require you to supply your email password. Neither option is all that attractive. Now there is an alternative. Google have recently added the ability to access the IMAP/SMTP features of particular Gmail account using OAuth.