In the silent film The Cabinet of Dr. Caligari, I love the way that they use shadows in the scene where Cesare murders Alan. You see Alan laying in his bed, then see a very large shadow emerge next to him. You don't see Cesare at all during the scene, and I think that that is very effective. You can skip forward to the scene in this video, it starts at about 5:38. It is very short, but it one of my favorite moments in the film.
Another way that shadow is used in film is to add a spooky effect, like in Nosferatu.
The shadows exhaggerate Count Orlok's already grotesque features such as his very long fingers, and it adds a really creepy tone to the whole scene by only seeing him in shadows. There is also a really neat part where the shadow of Count Orlock's hand seems to squeeze the girl's heart.
In a scene that is similar to the scene from Caligari, you see only a man being attacked in the shadows. Except this time, it is Boris Karloff and Bela Lugosi, and Lugose is apparently peeling the skin from Karloff's face. This is definitely an example of how what you don't see is much creepier that what you do see. Because we aren't getting a closeup of Karloff's face when it happens, we imagine it to be much worse than it is, and thus, it is scarier. I think that this scene is very effective, and was quite ahead of its time for the horror genre. The scene starts at about 5:34 in the video.
In the 1942 film Cat People, shadow was also used due to lack of special effects. In the scene where Simone Simon's therapist kisses her and she turns into a panther, they couldn't show a An American Werewolf in London style transformation. For one, it happens very quickly in the movie, and two, it was made in the early 40s so there wasn't special effects that could do that, especially since she turns into an actual panther and not someone in a makeup like The Wolf Man. However, it is still a great scene and I wouldn't have it any other way. You can watch the scene HERE.
To this day, there are still horror films that make great use of shadows. My favorite example of this is in Bram Stoker's Dracula.
In this film, Dracula's shadow has a life of its own, which is some of the coolest imagery in this movie. The scene, for example, when he is talking to Johnathon and his shadow appears to be strangling him. The only video that I found of this is dubbed in some other language, but you don't need to hear what he is saying to appreciate the great shadow effects in this scene. It starts in the video at about 5:04.
Another example is in the movie 1999 movie Sleepy Hollow. I couldn't find any pictures or a video of the scene I have in mind, but it is in the scene when the Headless Horseman is attacking the Killian house (the house full of redheads). When he goes for the wife, all you see is her face staring at him afraid, and the shadow of his axe moving up her face, and then a thud when it cuts to the shot of her little boys face. I think that it is extremely spooky the way it is, and much better than if they showed the Horseman raising his axe.