How to use your Google Apps email address (and your domain) with Zendesk.
Full tutorial on http://blog.getvladimir.com/2014/01/how-to-use-google-apps-email-address.html
Update: Since the Google Apps interface is changed, to get to the Email Routing now you will need to login to admin.google.com and:
1. Press on the "Apps" icon
2. Choose "Google Apps"
3. Press on "Gmail"
4. Scroll down and press on "Advanced settings"
5. From the top menu, choose the "Default routing" tab
The procedure still works.
The Custom Header you need to add for the email to work is:
X-Orig-To
Make sure to write it with uppercase and lowercase letters and without spaces, exactly as it appears in the video.
You can find the TXT values you need to copy and detailed instructions here:
http://blog.getvladimir.com/2014/01/how-to-use-google-apps-email-address.html
More info on SPF can be found here (thanks to +Victor Chávez for the suggestion):
https://support.zendesk.com/hc/en-us/articles/203683886-SPF-Learn-More