Is Intel's NUC with the Intel Core i3 3217-U (CPU) and HD4000 (CPU) capable for 3D game development?

If Unity runs on it, then you can make games using Unity on it.

It should, I run a 4 GB RAM Intel i3 370m with HD 3000 and I can do just fine. Just make sure to get Win7 rather than Win8 because ATM Win 8 isn't really that great for development of any sort (Just advice)

^ This basically, if it runs unity you can build stuff on it, but it might be severely limited in efficiency when you start building worlds with high-polygon models (or a bunch of low polygon ones) or play-testing. I'm also a bit puzzled to see someone with a 1.8 Ghz i3 and no dedicated GPU have 16 gigabytes of RAM, since your CPU and lack of GPU will bottleneck any real rendering or graphics related task.

So yes, technically possible but (very) sub-optimal. If you're looking to get at least somewhat serious you should consider getting a cheap i5 computer with a decent graphics card (shouldn't cost you more than 500/600 euros or your local equivalent).

Thank for the replies guys, i am from Greece as a matter of fact... I am a college student and i am always on the way so i want something as much portable as it gets (as such) without the limit of the resolution and of course the high price...at least i wanted... I change my mind during the day (after many hours of struggling with a little yellow notepad about pros and cons (TED! "How i met your mother"!!)) and i am gonna build a desktop computer instead... I will keep my Lamborghini VX6 for the way... Thank you again...

u can do it on ACER Aspire E5-575G-31MD win. 10 1tb ram and 4 gb (intel core i3 inside)