Problem :
I was trying to get my WCF project with SharePoint 2010 beta product. I had my database on other server. My development server was hosting WCF and SharePoint.
When I run it I started getting following error: Login failed for user <<domain>>\<<server name>>$
Workaround/Solution:
It will need to add user ‘NT AUTHORITY\NETWORK SERVICE’ to your database to get rid of this problem.
An asp.net application is running under NT AUTHORITY\NETWORK SERVICE account.
aanuwizard.com 
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Christian, iwspo.net
Hi, I can’t solve the problem with your advice.
You’re right, .net uses Network Service but if th eDB Server run on another machine adding Network Service would result in the Network Service of that machine, how can I add the correct user of my application server to the DB Server?