I have DBA databases on my servers as well. Doing much the same things that others have described. Absolutely essential.
In addition to all the private DBA stuff, we do collect some information that we want others to see. For example, we use Service Broker to capture Event Notifications for blocking and deadlocking.
For anything we want to make public we create views or functions that cover what we want to expose and grant access to developers and other support staff. This is still a DBA database, but the DBAs are providing details that others can use to improve their systems.