We know that Hindu texts do mention about demonic beings like Rakshasas. But is there any reference to ghosts in Vedas?
If ghosts are just 'atman' without bodies, don't they reincarnate?
Yes, they do exist in Hindu beliefs. Like people worship gods, there are also people and occult practitioners who worship ghosts. It is evident from statements like below in the Bhagavad Gita:
yajante sāttvikā devān yakṣa-rakṣāṁsi rājasāḥ
pretān bhūta-gaṇāṁś cānye yajante tāmasā janāḥ [BG - 17.4]
Men in the mode of goodness worship the demigods; those in the mode of passion worship the demons; and those in the mode of ignorance worship ghosts and spirits.
yānti deva-vratā devān pitṝn yānti pitṛ-vratāḥ
bhūtāni yānti bhūtejyā yānti mad-yājino ’pi mām [BG - 9.25]
Thos who worship gods go to the gods; worshippers of forefathers go to the pitru loka; to the ghosts go those who worship ghosts, and those who worship Me come to Me alone.
Ghosts do reincarnate, but a jivatma becomes a ghost for multiple reasons and until he obtains a womb for rebirth he will have to wander as a ghost. Depending upon his karma and spiritual activity the length he stays as a ghost can vary.
When a person dies then he becomes a preta (Ghost). Generally this phase is temporary and as soon as the funeral rites are over, the preta state is over and the jiva then gets the status of Pitru (manes or forefathers). However, if the funeral rites are not duly performed or the death and actions of the person is not good then he may get stuck in the limbo or preta phase:
pāpakarmaratā ye vai pūrvakarmavaśānugāḥ
jāyante te mṛtāḥ pretāstāñchṛṇuṣva vadāmyaham [GP - 2.22.3]
He who is indulged in sinful activities goes to become a preta after death; that I am telling you please listen.
svaiḥ svaistu karmabhiḥ prāptaṃ pretatvaṃ hi dvijottama
paradroharatāḥ sarve pāpamṛtyuvaśaṃ gatāḥ [GP - 2.22.33]
O best among the twice-borns (dvijottama), one certainly attains the state of preta due to ones own actions. All those who are engaged in offence or enmity (droha) toward others, under the influence of sin and death go on to be come ghosts.
That chapter then describes many such activities doing which one goes into the preta state for certain. Basically if one commits sins, kills other, causes pain to elders, brother, sister etc. without any reason, who has forsaken rememberance of Vishnu, who doesn't perform fire sacrifices, etc. obtains the state of pretatva (ghost hood).
Do ghosts and spirits exist in Hindu beliefs?
Gurudev, Shiva is called Bhoothnath (lord of the ghosts) and he is surrounded by ghosts and spirits. Do ghosts really exist?
Sri Sri Ravi Shankar: If you ask me whether Shiva exists, I can answer, yes! But I don’t know about the ghosts around him (laughter).
Yes, ghosts do exist but they are not different from him. They are in him. The 5 elements are known as the Panchabhutas. So Air, Water, Fire, Earth and Space are collectively called the five bhootatmas. Some souls also become ghosts and that is because even after leaving the body, they are not able to drop their vasanas (impressions due to cravings and aversions of the mind). That is because even after the soul leaves the body, the realization does not dawn that it is the eternal light, or consciousness.
It is like, the food is in front of them and they are thinking of eating but they can’t actually eat it. The word ‘Bhootkaal’ means the past. This is because it has already passed, but still one is holding on to the impressions of it and unable to drop it. Ghosts are also souls but they have lost their power. They are powerless as they have not realized that they are souls. When the soul attains self-knowledge, then it becomes powerful. When they realize this, they no longer remain as ghosts (they are called earth bound souls).
From a Q&A with Sri Sri: http://officialsrisri.blogspot.in/2014/12/gurudev-shiva-is-called-bhoothnath-lord.html