As described in this connect article there is an issue with the integration of SQL Server 2008 Express Edition ans Visual Studio 2008 if you are running on an x64 system (the OS itself! Not runing 32-bit Vista on a Core 2 Duo) (although some report this bug on a 32-bit OS).
This issue is currently unresolved, but you still can open the database in the server explorer if (and only if) you modify the connection string NOT to use a User Instance.
You can do this by rightclicking the database in the server explorer, modify connection and set ‘User Instance’ to ‘False’ (last item)
User Instances are not allowed anymore since SQL Server 2008, as described here.
In order to make it work as it should be you can either install a 32bit SQL Server 2008 Express (which I do) or do as described here.
Update: Back to SQL Server 2005 Express Edition, all the rest fails as described.