Where are registered servers stored?

For Windows 10 and SSMS version V17 the document can be found using this path in windows explorer

%APPDATA%\Microsoft\SQL Server Management Studio

Or this powershell command

dir "$env:APPDATA\Microsoft\SQL Server Management Studio\RegSrvr.xml"

    Example
    Directory: C:\Users\george\AppData\Roaming\Microsoft\SQL Server Management Studio


Mode                LastWriteTime         Length Name
----                -------------         ------ ----
-a----       19/02/2019   4:04 PM          60998 RegSrvr.xml

They are kept as an XML document here:

%APPDATA%\Microsoft\Microsoft SQL Server\100\Tools\Shell\RegSrvr.xml

On Windows XP this resolves to:

C:\Documents and Settings\username\Application Data\Microsoft\Microsoft SQL Server\100\Tools\Shell\RegSrvr.xml

Note: As of Windows Vista there is no Application Data folder, and the path resolves differently.

In windows 8 and 7 here is the correct path.

C:\Users\username\AppData\Roaming\Microsoft\Microsoft SQL Server\100\Tools\Shell\RegSrvr.xml