Am I the only one who finds this 'feature' to be a huge marketing embarrassment for Microsoft? The entire point of Windows was the GUI! Microsoft hung its hat on the fact that its  product made the computer so easy to operate, anyone could use it. No longer would someone have to memorize an endless volume of commands to use a computer. Now, Microsoft is essentially saying that the one feature that made its buggy, crash-prone, blue-screening, memory-leaking, vulnerable software worth having is a feature NOT worth having. To me, this akin to Apple dropping the iPad to pitch a new 1970s-style clunky pc, complete with a CRT monitor, as the way to go. If I'm going to go without a GUI as an administrator, the LAST product I'm going to use is Windows. I'll run Unix and save myself a fortune in cost, headaches, and security vulnerabilities.
-Todd
Personally, I love it. The problem is that there's no way to turn it off and back on (without reinstalling). It would be nice to start in the full version and then (assuming it's possible) switch to Core. And vice-versa.
Many roles and software don't run under Core, but hopefully MS will make that better as time goes on. Because of this it does make me nervous (as a consultant) as we could start off using Core then find something doesn't work or have the customer change the requirements and have us stuck with reinstalling. But we do use it often and it does help performance. Also note it theoretically requires fewer reboots, thus leading to better uptime and it has a smaller attack surface.
-Mike
I may be getting a bit old too, but I seem to remember that the move away from NetWare, etc. to Windows servers in the '90s was sparked by the server having a GUI in the first place. One interface shared between the desktop and server for less training, easier configuration, etc. Sounds like Microsoft has been spending some time with Linux!
For those of us who have never embraced the WinTel platform as the only show in town, it's not a big deal. Linux servers, Unix servers, and even the odd remaining NetWare server still rely more on the command line interface than a GUI. Microsoft is just coming back to the fold.
You could see it coming too. First there was VBScript, then the move to PowerShell, and now Server Core.
-Glenn