Shape is my favorite design principle for good reasons. Two of the most essential laws of design are unification and contrast (and no, I can’t substantiate using the term "laws," but I’m going to anyway, because I’m right, darn it). Unification deals with the visual continuity of a design, and contrast deals with the differentiation of qualities across that design.
First, let's assume that the goal of character design is appeal. And from what I’ve seen, the character designs people find most appealing are 1. Easily read and understood, and yet 2. Have some unique or unpredictable qualities. People like to feel some familiarity with a character, but they expect to see something that feels new. The law of unification can make designs readable, tying even complex designs together in interesting ways. The law of contrast also improves readability by placing emphasis on what’s important and diminishing what isn’t, but also, the right contrasts can generate that sense of uniqueness and unpredictability. Balancing unification and contrast is hard, but they’re important in creating appealing characters.
Fortunately, while balancing the two laws is tough, the principle of shape can be a powerful tool for working unification _and_ contrast into a design. You can unify a design using echoing shapes, complimentary shapes, interlocking shapes, or shapes that share contour lines. You can then add interest to the design using shapes of contrasting size, type, rotation, proportion, and spacing.
These examples are from a side project I volunteered for. I wanted them to draw upon stereotypes—so I didn’t add a lot of unpredictability to the content of the characters. Instead I tried to put interest into their shapes and other elements. With the Igor character, I used like shapes to unify the character and reinforce his heavy, dejected persona. I used a variety of shape sizes, however, to add that little bit of visual interest. I also spaced the shapes unevenly to add some unpredictability. The mad scientist, on the other hand, uses a larger variety of shape types, but they are unified by fitting them within his squarish frame. I also used connecting contour lines to pull the shapes together. The woman uses both like and varied shapes, and contour lines connect them together. I'm not sure the other designs are worth talking about, and that baby is just disturbing.
Well, sorry if that was long. Hope someone finds it helpful. Or even if it sparks discussion, good. Either way, it's always fun writing these.