General:
* Ghost
* Phantom
* Apparition
* Wraith
* Spirit
* Haunt
More specific:
* Vision (if it's a visual hallucination)
* Hobgoblin (if it's a menacing or frightening spirit)
* Shade (if it's a shadowy or indistinct figure)
* Bogeyman (if it's a terrifying figure used to frighten children)
* Ethereal (if it's otherworldly and intangible)
The best synonym depends on the specific context and the type of specter you are referring to.