If working in Gnome, click in the top right corner by your user name and choose the Online Accounts, you can connect to your social media accounts. If you connect your google account, it is possible to sync calendars, mail and contacts.
When you select google account and click add, I get this error:
"Error getting request token: bad request"
OpenSuse 12.1, Gnome 3.2
I see that the error is likely related with the network settings or firewall, but can handle himself yet.
The problem is not with your network settings/firewall. This bug appeared with the first release of GNOME 3.2 and quite famous, I encountered him. Two identical PCs with identical Arch Linux on one he was shown, and the other is not.
Try updating GNOME a separate repository, because after several updates the bug is gone in Arch and Fedora.