Windows Authentication for a non-local non-domain Login I have SQL Server 2008 R2 installed on a Windows Server 2008 R2 box.  There is no domain in the network.

Is there any way for me to add a Windows Login on SQL Server for a non-local and non-domain user?  For instance, if the server is Server1 and a PC on the network is PC1, how can I add PC1\User1 as a Windows Login on the SQL Server instance installed on Server1?
Create matching usernames and passwords. It really is that simple. For your example, create an account for User1 on Server1 with the same password as on PC1.

Just in case this is an issue you're having with connecting SSMS with a non-domain account, that requires jumping through an additional hoop. Some applications don't support stored usernames and passwords via the windows credential store. SSMS is one of them.

I have a bunch of runas shortcuts to deal with connecting SSMS to a variety of servers in different domains:

C:\Windows\System32\runas.exe 
/netonly 
/user:DOMAIN\USER 
"C:\Program Files (x86)\Microsoft SQL Server\100\Tools\Binn\VSShell\Common7\IDE\Ssms.exe"


You could also make use of the SysInternals ShellRunAs extension.