Here's a new SharePoint 2007 error message. I tried to browse to a site and got the following error:
Operation aborted (Exception from HRESULT: 0×80004004 (E_ABORT))
This one turned out to be because the application pool's account had lost (still haven't figured out how) permissions on the appropriate content database. Being lazy, I just gave the account db_owner permissions on the content database. Not the most secure resolution, and I should bother to look up the proper credentials, but this solved the problem.