I just came back from watching "Gothika". First of all, its genre is both horror and, well, thriller. But every (good) horror movie has its very own style on how to be frightening. Just like Stanley Kubrick's The Shining uses the sinister music and The Exorcist tries to be frightening by letting the obsessed girl use a lot of swearwords (which makes it no frightening at all, but more like boring, or at the best, funny, or are you frightened by "your mother sucks cocks in hell"?
)), Gothika uses the element of surprise, and that makes it extremely frightening and gray. In fact, this is the very first time in a horror movie that I actually heard people (not just women, but also men) scream out loud because they were so frightened.
I'm not going to tell anything about the movie's content, I can only recommend to watch it for yourself and be frightened by yourself.
Besides the horror part, Gothika also tells an important lessons on how repressive asylums are, and that it's virtually impossible to escape from system as soon as you are marked as "lunatic". The following quote from the movie expresses this really well: "You can't trust a person who thinks you are insane." (rough translation, I saw the movie in German).