Windows Server 2008 Core
You can administer a Server Core machine using the command line - there are many new and enhanced commands available in Server 2008 to facilitate command line administration - or graphically from another machine via MMC. The idea is that these core machines will be used for specific pre-defined server roles, with all extraneous features removed. This allows for a smaller footprint, better performance and improved security out of the box.
Though designed for pre-defined roles and not applications, there is nothing to stop you installing your own software on these machines if you're comfortable with the interface. To me Server Core makes an ideal secure high-performing host for Informix Dynamic Server. In the lab we experimented with installing IDS 11.50, CSDK 3.50 and OpenAdmin Tool 2.20 on a Server Core image running on Virtual PC, and they installed with no problems. I also installed a copy of Firefox Portable so I could run OAT directly on the machine, though it would make more sense to run the browser remotely.
OAT running on Server Core
I see Server Core as having a lot of potential as a backend machine running IDS, or as an appliance running under Virtual PC with a complete solution installed, for example: Windows Server 2008 Core + IDS + CSDK + < Insert solution here>.
What I would really like to see is a way to create portable appliances like this that could boot from a USB drive, but in the meantime it's easy to play around with different configurations using Virtual PC.