What kind of characters do you like to read about?
One of the author discussion groups to which I belong recently asked the inverse question: what kind of characters do we, as authors, like to write about? The other authors all gave really good, if somewhat different, answers to this question. Everyone agreed that characters should be realistic, with flaws and imperfections just like people we meet on the street. Of course, a story about an ordinary character, in an ordinary setting , on an ordinary day, doing ordinary things will be, well, pretty ordinary. So, unless one has the talent to produce a masterwork like Ulysses which does exactly the above, there must be something about your character that inspires the imagination.
Sometimes the character might have unusual abilities. Good Will Hunting is an excellent example of a story in which a character from an ordinary background has extraordinary abilities. In other cases, we find ordinary characters in extraordinary situations. The Birds is surely such a tale, in which an extraordinary event challenges both the characters and their social matrix. Sometimes the characters might be in a setting which is culturally or historically remote from the reader, so that what is ordinary for the characters is unusual for the audience. Much of science fiction and fantasy fall into this category, as does historical fiction. The point of this is that in an interesting story characters confront a challenge. Sometimes the character is successful, sometimes not. Sometimes the character changes and grows, sometimes the character's flaws lead to a tragic denouement. In the best cases, the fictional conflict engages and changes something in the readers.
In order to inspire the imagination, characters must exhibit traits for good or ill that the reader can recognize. In novels with both a protagonist and antagonist, both must represent believable types that the reader can love or hate. In more complex works, such as Anna Karenina, good and evil may be at war inside the characters and this internal conflict drives the story forward.
It's clear that there are lots of things that can make a character interesting. Even the most insipid character, when thrust into an unusual chain of events, can become interesting -- think of North by Northwest, for example. Alternatively, the most dynamic and charismatic of characters stuck in a prosaic setting with no conflict is boring. Superman is interesting only when his super-powers aren't up the challenge!
This brings me to my answer to the question about what characters interest me. All of the other answers are interesting and weave together to make characters I'd want to read and write about, but what most interests me are the relationships of my characters. When Gene Siskel reviewed movies, one could always count on him to like movies with strong relationships. His instincts coincide with mine exactly. The relationships among the characters, between the characters and their culture, between the characters and their physical world -- this is what I find most interesting. Relationships reveal the internal depths of the character, expose conflict, and generate change. The physicist Arthur Eddington once said:
We often think that when we have completed our study of one, we know all about two, because "two" is "one and one." We forget that we still have to make a study of "and."
This insight applies as much to real -- and fictional! -- people as it does to mathematics. We all live in and interact with the world about us. Even before Friday's arrival, Robinson Caruso confronted and surmounted obstacles in his world. These conflicts, and his reactions to them, both exposed his character and set the stage for internal growth.
So, my answer to what kind of character I find interesting is that I am less interested in the character than in the relationships between the character and the world about him.
