General:
* Ghost
* Phantom
* Spectre
* Spirit
* Vision
* Wraith
* Ethereal being
* Manifestation
* Appearance
More specific:
* Haunt (if the apparition is associated with a place)
* Shade (a less threatening, more ethereal ghost)
* Doppelganger (a ghostly double of a living person)
* Poltergeist (a noisy, mischievous ghost)
* Bogle (a mischievous or malevolent spirit)
* Ghoul (a ghostly creature that feeds on corpses)
The best word to use will depend on the specific situation and the connotations you want to convey.