09:53AM: It appears as the issue has gone away after reporting it to Google. We'll continue to monitor.
09:45AM: We have confirmed that completing the CAPTCHA appears to resolve the issue on a per-computer basis. Clearing caches and cookies will make it reappear.
09:40AM: Some Google Drive documents, if they even load, are sticking on Trying to connect...
09:35AM PST: We have received scattered reports (and have experienced it in our office) of Google suddenly requiring a CAPTCHA to access Google Drive or Sheets. It is unclear if this behavior applies to other Google Apps as of yet, but Google Mail appears to be unaffected. This appears to be related to one of our public IP ranges, but Customer Care is investigating.
Below is an example of the CAPTCHA window: