One reason Frankenstein and Frankenstein's creature have had such a hold over us for two centuries is because many people can relate to this creature. He is alienated from society, judged and scorned, an outsider, and an outcast. It would be difficult, I think, to find a person who has never felt this way (though, perhaps, to a lesser extent). Further, the fact that the creature justifiably blames his father, Victor, for many of his problems may be easy to relate to for many readers as well.
Another possible reason for this story's continued relevance to us has to do with the questions of scientific ethics that it raises. Is Victor right to try to create life in this way? Is he trying to "play God"? Should that stop him? Even now, people talk about creating "designer babies" whose physical traits (such as sex, eye color, and hair color) are chosen specifically to please their parents. Is there an ethical dilemma to these kinds of choices? Where is the line? Just because science can do something, does that mean it should do it? What is our responsibility to a baby who doesn't turn out exactly the way we think it will? Even 200 years later, we still struggle with the same kinds of ethical quandaries Shelley appears to have been ruminating on.