I am working on a C# 4.0, WPF 4.0, SQL 2008 project and I do work at home and in the office. I just setup SubVersion using Visual SVN per the recommendations found in other ques
Simple: Don't put the connection string in code, read it from configuration data somewhere. And then just don't put that configuration data in Subversion.
In an app that I'm working on now, we store connection string information in the Windows registry, in HKLM\Software\[OurProduct]\Database.