I get hundreds of these messages in my SQL Server logs every day (Exactly every 15 minutes).
The messages have a sev 14 and a state 16, I have been searching the web for answers, but have drawn a blank thus far.
One suggestion was to run a SQL Profiler trace.
I did this and found that the ApplicationName is 'Microsoft Windows Script Host', but when I checked the Task Manager on the server, the ClientProcessID specified in the Profiler trace does not appear in the list of PIDs.
I have also checked my Logins, and NT AUTHORITY\SYSTEM is present and enabled, and it has a server role of 'sysadmin', so I cannot see why the login would not be able to access any of the databases.
Also, I have checked all Jobs to check any blank DB name (As a suggested solution) But I found nothing.
Any help in tracking this down would be greatly appreciated.