What minimum level of credentials are normally required to join a member server to the domain?

Solution 1:

By default a domain user can add up to 10 computers to a domain. There is a way that administrators can restrict this default behavior to only allow Administrators to add computers to the domain, by using ADSI Edit.

http://support.microsoft.com/kb/243327

Solution 2:

By default Authenticated Users are assigned this privilege.

This is defined by a GPO:

Computer Configuration --> Policies –-> Windows Settings –-> Security Settings –-> User Rights Assignment --> Add workstation to domain

As noted by @redknight, by default users (excepting domain admins) are able to join 10 computers to a domain.

Solution 3:

"Add computers to domain" is not restricted to Domain Admins at all, that wouldn't be very good security. There is also no distinction between adding a workstation, or adding a member server.

This article describes some of the details.