It just weird, when you are using SQL Server EXPRESS 2008,
you can Add Database Server, no more "Connections to this edition of the database server are not supported"
And, no.
What we are talking about is not "Add Database Connection", but Add Database Server.
Add Database Connection just both works on SQL Server 2008 and SQL Server Express 2008.
Why we resist to use Add Database Server, and consider it as important is because:
to set privilege of ArcGISSOC user when we are using ArcGIS Server to create web editable map service layer (feature-access).
In the manual help of ArcGIS Server, for ArcGIS server could use feature access properly,
we have to right click the Database Server, and then select Permissions,
and set ArcGISSOC user as user and admin on that database server.
When we use SQL Server Express 2008, we could do that without problem.
But on SQL Server 2008, we can't.
Is it a bug?
We need to use SQL Server, not SQL Server Express,
because the Express one has limitation: only single core used, only support 4 GB database, and more limitation.