Update: It looks like various services are starting to come back again, but with some glitches (such as the address bar in Gmail not working correctly). A Google spokesperson has now provided us directly with a statement about the outage:
Today, at 3.47AM PT Google experienced an authentication system outage for approximately 45 minutes due to an internal storage quota issue. Services requiring users to log in experienced high error rates during this period. The authentication system issue was resolved at 4:32AM PT. All services are now restored. We apologise to everyone affected, and we will conduct a thorough follow up review to ensure this problem cannot recur in the future.