Children seem to be great fodder for many films that use ghosts as major villains, so to speak, or as very large plot points. The 1961 film, The Innocents, is a good example of children being terrorized by ghosts. The Innocents is based on the 1898 novella The Turn of the Screw by Henry James, which was later adapted by William Archibald into a play in 1950, which is what the film is based on.
In this particular film, the ghosts that appear can be viewed as villains. It is ultimately up to the viewer to decide that the ghosts are real, but the film seems to present them in a way that they are real. The ghosts are former employees of the home that the film takes place in, and both seem to have died under unfavorable circumstances. The ghosts are seen by the governess, named Miss Giddens in the play and movie, in which she is played by Deborah Kerr, and it is also possible that they are seen by the children that they are there to haunt.
The major ghost is the ghost of the character Quint (Peter Wyngarde). He is in the estate to haunt the young boy Miles (Martin Stephens), with whom he shares a past. Miles ends up dying towards the end due either to the ghost of Quint or the governess being so terrified at "seeing" the ghost that she has suffocated Miles. Quint's ghost could be classified as a malign spirit, and it seems to ultimately achieve its goal.
The concept of ghosts appearing to children, trying to kill children, or actually being children is no new concept as far as films go. The Innocents probably helped start this trend in film. Some of the more major recent films using elements like this would be The Ring (both the US and Japanese versions), Ju-on (a Japanese horror film), and The Sixth Sense. Each of these films is a great example of an obviously old concept in film and literature.