Can Lego bricks be connected diagonally?

Despite the Lego movie being advertised as the first ever feature length Lego film, there have been Lego films before, such as Clutch Powers. When watching the film, I noticed that Clutch says Lego bricks can never connect diagonally, and yet Moc makers achieve angles in their creations by attaching bricks diagonally all the time! Which brings me finally to the point of this post, a picture of one of my mocs. What is it? I don't know, but it looks cool!