Simple rotation... impossible? I'm feeling crazy, why is it so hard to just rotate objects predictably in blender? 
No matter what setting I use, I cant get things to rotate how I want to.
Watch these two webms. Imagine the front beveled face is the face of a human and I want him to look up = rotate his head back a bit.
It would stand to reason that blender has some kind of internal object rotation right? Well that setting doesnt work either. Nothing works for me.



Pathetic attempts to make it work but I cant:

http://webm.land/media/reS6.webm

http://webm.land/media/9cqn.webm
It looks from your video as if you are rotating on the Global (World) axes, where what you would like is a rotation of the cube about one of its own local axes. If you haven't reoriented the cube in Edit Mode since it was created, its local axes will still run from the cube's center through the centers of its faces.

In that case, as you have, you can just set the Transform Orientation (in the header at the bottom of the 3D View)  to 'Local'. Set the pvot point to the center of rotation you want ..(e.g. 'Individual Origin(s))

The primary, default, orientation for transformations is always Global. To reach the secondary orientation ( the one in the header ), you have to hit the constraint key(s) twice. So hitting RXX, RYY or RZZ  will let you rotate the cube around its local axes.

(If you rotate all or part of an object's mesh in Edit Mode, that's all you have rotated. The object's local axes remain where they were before the edit.)