Some ghost stories in the ancient world
Patroclus in the Iliad by Homer
Ghosts in the underworld visited by Odysseus and ghosts of the suitors at the end of the Odyssey by Homer
Clytemnestra in the Eumenides by Aeschylus
Hector, Creusa, and Anchises in the Aeneid by Virgil
Laius in the Thebaid by Statius
Julia in the Bellum Civile by Lucan
Cynthia in Propertius 4.7
Plutarch's Life of Cimon 1.4-2.2
Lots of ghost stories in Apuleius—the opening of The Golden Ass is especially fun
Ovid’s story of Ceyx and Alcyone
Hearing ghosts of soldiers at Marathon, Pausanias 1.32.3
Tacitus Annales 1.65
Ammianus Marcellinus (31.1) has the ghosts of the King of Armenia and others appear as omens to Valens' death
Agrippina haunts Nero in both Suetonius and Seneca’s Octavia
Not an actual 'haunting', but Plautus' Mostellaria could be a good example of the prevalence of 'ghost stories'
The sinister figure in Herodotus book 7 who threatens to burn out Artabanus' eyes with hot pokers!
The gnat to the shepherd in the pseudo-Virgilian Culex
Philostratus's Heroikos has a disturbing story about Achilles appearing centuries after the Trojan War to kill the last descendant of Priam
Suda s.v. Euthymos is about a ghost/hero demanding the life of a young woman every year.
There’s something called the taraxippus, which was a ghost that scared horses at hippodromes and caused them to crash the chariots. Various ghosts for various hippodromes.
There's also that brief little section about the "haunted house" Augustus was born into in Suetonius' Life of Augustus (section 6)
Tantalus at the beginning of Seneca’s Thyestes
The ghost story at Phlegon of Tralles FGrH 257 F36 is absolutely killer
Lucan Book VI; Erichtho forces a ghost to reinhabit its dead body and prophesy.
Suet. Cal. 59 about Caligula’s ghost
Pliny the Younger, Letter 7.27
The ghost of Polydorus in Euripides’ Hecuba
A New Kingdom story about a ghost haunting the Theban Necropolis
Darius in Aeschylus’ Persians lamenting the downfall of his line
Lucian of Samosates Philopseudes
Plutarch's Life of Cimon 1.4-2.2. He doesn't go into details about the haunting but it's a great story about a man called Damon of Chaironea (1st C BC) who murdered a Roman official, became a bandit for a while, was murdered in a bathhouse
Debbie Felton's Haunted Greece & Rome (U. Texas, 1999) is a good starting-point for this topic.