I rather like characters who are "grey" - people who are imperfect but try anyway. People who might be right or might be wrong, depending. People who struggle (even with inner demons) against odds, the kind of person we want to cheer on. People who we would like to be or know...maybe. People who have courage or just brass. People who stand up for something, hopefully what's right. Ordinary people who do extraordinary things; extraordinary people who have ordinary problems just like me. I like up endings, so I like characters who ultimately win - but sometimes (like "Rocky"), winning can mean different and unexpected things. I especially like richly drawn characters who I sometimes love and sometimes hate, characters that surprise me but never really disappoint me.
In writing, I like characters that are so vivid that I'm right there in the scene, watching them play it out and scribbling as fast as I can. In reading, I like characters who take me on some sort of adventure and sort of let me tag along.