This week's favourite brick is an old hinge that I don’t see used much anymore. Despite this, the finger joints hinges have some advantages over the ones we commonly see today.
As shown in the picture, these finger joints are great for hinges where plates or other pieces are positioned directly adjacent. By this, I mean that because of their flat profile, other bricks can be built on them, unlike the newer hinges which have an extrusion preventing this.
This technique has many applications, but a good one mentioned by Tammo S. on Flickr is an angled wall. Credit to him for the images pictured as well, which you can check out here: https://www.flickr.com/photos/tammo_s/27349360857/in/gallery-37217189@N04-72157633532233362/