A well-designed character should have typical traits. These include physical appearance, as well as emotional attributes. Typical ways of speaking (e.g. Mr. Mickawber in Charles Dickens's "David Copperfield") or typical phrases add to an interesting character.
Of course, a character can show completely different moods in the course of a story - in genres such as the cartoon, often you can see abrupt mood changes within just one second. This is in fact quite popular as it is funny to watch. A mood change does not mean that the character changes, but it allows you to see the character's personality from a new side. Therefore it adds to a complete picture.
In comics and cartoons, the art of creating a new character is called character design. These characters have a great potential for merchandizing products. Character designers produce model sheets for other artists that show the appearance of the character from all sides and the exact body proportions, as well as any peculiarities. These days, often 3D models are created on the computer.