I have to be able to feel with and understand the characters. That's why I tend to stick with historical fiction because I love history and that's why I find it more interesting than say a romance novel.
However I have a really hard time not finishing a book even if I'm not really into it. I think there are only a handful of books that I have never finished. In most instances if I don't like the book then I will leave it for a later time and by then I will hopefully enjoy it then.