We're not exactly talking about Gryffindor Tower's Nearly Headless Nick here, but there are definitely some haunting figures in Wuthering Heights. It is important to note, though, that Brontë's ghosts are ambiguous entities and may have logical, rather than supernatural, explanations.
Take Catherine's ghost at the beginning. This paranormal figure with the icy hand who claims to have been "a waif for twenty years," (111.55) could just be a figment of Lockwood's nightmares. Still, when Heathcliff demands an explanation for the commotion in the oak-paneled bed (which he clearly thinks involves Catherine's ghost), Lockwood answers that Wuthering Heights is "swarming with ghosts and goblins!" (3.67). As readers, we accept his interpretation because Lockwood is our narrator, but his characterizations can also be wildly inaccurate, reflecting his own biases and assumptions, as with his description of Catherine's ghost as a "little fiend" who may have been seeking entry into the window in order to strangle him. As he further describes her, "And that minx, Catherine Linton, or Earnshaw, or however she was called – she must have been a changeling – wicked little soul!" (3.69).
In many ways the ghosts in Wuthering Heights symbolize a lack of closure for the lovers. Heathcliff wants to believe in ghosts and the afterlife because that means Catherine will still be around. When Catherine dies, he begs to be haunted: "I know that ghosts have wandered on earth. Be with me always – take any form – drive me mad!" (16.25). Brontë's ghosts are not your average Gothic novel device, as they seem to have much more to do with romance than evil. The superstitious Joseph may be the only one to see the ghosts as sinister.
At the end of the novel, Nelly Dean tells Lockwood that the "country folks would swear on their Bible [the ghost of Heathcliff] walks," and they report having seen him "near the church, and on the moor, and even within this house" (34.99). These reports could go either way. That the villagers see the ghosts too could mean that they are not just figments of Lockwood's imagination. On the other hand, the villagers may just be demonstrating the same kind of superstitious fear as Joseph. Even drama-loving Nelly is skeptical about the existence of ghosts. When a neighborhood boy reports "They's Heathcliff and a woman, yonder, under t' Nab [...] un' Aw darnut pass'em" (34.101), Nelly tells Lockwood that she did not see the ghosts herself and that "He probably raised the phantoms from thinking, as he traversed the moors alone, on the nonsense he had heard his parents and companions repeat […]" (34.103).
So what's the verdict on the ghosts? Brontë leaves it up in the air, but the hauntings and uncanny happenings are part of what make the novel so riveting.