I got my Dad a NUC for Christmas...He hasn't really been using it yet. I think this might have been a more interesting and simple gift, wish it came out in time. I did get to play with the NUC because I wanted to have it all configured and ready to use. It was interesting to see how they got all of the components packed in and I was impressed by the performance. Main issue I had was graphics support, because I wanted to put Elementary OS on it to see if he'd be interested in trying out Linux. Ended up going with the latest Ubuntu instead (Elementary OS Luna is built on Ubuntu 12.04) which worked fine.
My Dad had gone through a couple of those Shuttle "Mini" computers (the motherboards were Flex-ATX, slightly bigger than Mini-ITX and obviously needed to be smaller than micro-ATX), so I thought the NUC (between Nano-ITX and Pico-ITX [1]) might appeal to him. They both died and he's currently using a standard desktop. I believe one or both of his Shuttle's died due to a PSU failure, so it's nice to have the external power brick on the NUC.
He and my Mom had previously been using a Windows Media Center desktop with a tuner card and Comcast cable, but they're using DirecTV boxes on all the TVs now so not much need for a HTPC. He said he was thinking about trying to use the NUC with Windows 8 and a touch screen somehow...Not really sure how he can accomplish that. Besides introducing him to Linux, I was thinking he could use it on his TV as just an alternate computer and wanted to show him how to use Synergy to control it with his desktop keyboard/mouse. He's currently switching his TV between the DirecTV box and his desktop as a second display.
At the very least it's a backup, and he could potentially take it on trips as a more powerful alternative to a laptop. There's just so many different options for computing these days. It's like information overload, but with hardware.
[1] http://www.anandtech.com/show/5800/slimming-desktops-down-in... (existence of Nano-ITX and Pico-ITX pointed out in the comments)