At Arc 10.1, "Add Spatial Database Connection" has been replaced with a more generic "Add Database Connection".
Whilst I appreciate this is better for connnecting directly to different types of databases, it means users can no longer easily create a new connection to an ArcSDE service.
To quote the 10.1 help:
"If you have connection files that were created prior to 10.1, they will still work. However, if you need to create a new connection to your geodatabase using an ArcSDE service, use the Create ArcSDE Connection File geoprocessing tool."
This is a much more long-winded process - some this simple should not require the use of a tool. Moreover, you cannot "Test Connection" like you used to be able to.
Alternatively, "ArcSDE" could be added to the list of possible options in the "Add Database Connection" drop-down.