An actual SQL post for a change
This is a pretty interesting blog from Microsoft about how networking works in SQL Server:
http://blogs.msdn.com/sql_protocols/default.aspx
I found them when I did a google search for a sql server error 18456. They're encoding the actual problem in the STATE information:
http://blogs.msdn.com/sql_protocols/archive/2006/02/21/536201.aspx
Of course, when you fail to log in using the SQL Server Management Studio it doesn't display state information, so this information is absolutely accurate and completely useless for trying to diagnose connection issues from the studio.