One example that's really fun is Inkblots. Making an inkblot and trying to draw form and personality out of it is not only fun but can lead to more developed projects. Like this guy and his Inkblot Monsters on Youtube:
There is no shortage of resources for learning character design. I find Youtube amazing for learning because I can direct myself related to my interests. Here are some examples of links that caught my attention and have to do with Character Design:
Another indispensable tool is sketching. It will help you develop your drawing and can in and of itself be a form of generating ideas. Here is an interesting example of an artist using Thumbnails as a development tool. It's in digital media in this case, but the principals still apply. Draw small noncommittal characters. By not getting caught up in the details you can get out lots of ideas.
Character Definition: Feature and traits that form the individual nature of a person (or personified. Personality.
Kinds of Characters/Character Uses: Cartoon Characters, Sports and Corporate Mascots, Comic Book, News Strip (See Practicalities) In design pipeline, working with a team
Caricature: A portrait or that exaggerates or distorts the essence of a person
Our Character: Think of uses and how to get across personality.
Research: When I was in Jr High School I went to a work experience program at a comic book artists' studio. I sort of expected to be drawing, but much of my time was spent researching and finding references for scenes in the comic. When designing a character start to collect not only ideas, but reference pictures of things that might appear in your character's world or be similar enough that they can inform your drawing.
Designers: If you're designing your character to be used with a brand, be sure to make colours and styles congruous.
Visual styles: Look at how other artists solve the problem. If you are interested in a specific genre don't be afraid to learn and appropriate.
Understand Audience: (Simple shapes and colours) Children/Adults, artists, designers, cultural groups, sensitive groups (hospital etc)
Exercises: Inkblot and Thumbnails