I get hundreds of these messages in my SQL Server logs every day.
The messages have a sev 14 and a state 16 (which I believe means 'login valid, but not permissioned to use target database'.
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 rol;e of 'sysadmin', so I cannot see why the login would not be able to access any of the databases.
Any help in tracking this down would be greatly appreciated.