(What is provided below has been taken mainly from The Psychology of Déjà Vu by Dr. Vernon M. Neppe [originally published by the Witwatersrand University Press in 1983]. His book provides far more information than can be summarized here and can now be purchased on-line as an e-book by going to http://www.brainvoyage.com/deja/PDV/ . Other writings of Dr. Neppe on déjà vu are available there as well.)

Definition

Dr. Neppe defined déjà vu operationally as being "any subjectively inappropriate impression of familiarity of a present experience with an undefined past". (p. 3) This is a very general definition and can be applied to all instances of what we now call "déjà experience". I would add, though, that surprise and a certain weirdness or uncanniness are also important elements of such experiences. Saying that they are "inappropriate", while very true, just doesn't quite fill the bill. MacCurdy, as Dr. Neppe says (p. 8), used terms like "bewilderment" and "perplexity" in connection with such experiences and I think most people would agree that déjà experiences are certainly bewildering and perplexing.

Categories of Déjà Experience

In 1964 Prof. C. T. K. Chari, former Professor and chairman of the Department of Philosophy and Psychology at Madras Christian College, published a paper in which he divided instances of déjà vu into three categories: 1) Pathological, 2) Normal, and 3) Precognitive and telepathic. Dr. Neppe divided those having pathological déjà vu into temporal lobe epileptics and schizophrenics.

I would like to offer my own category scheme (in the order of their [surmised] prevalence):

1. Normal
   These can be of short, medium or long duration (even continuous). The main features are that they mainly consist of an inexplicable sense of familiarity but involve no paranormal (i.e., precognitive or telepathic) elements nor are they associated with any pathological condition. As psychoanalysts have pointed out, though, they may serve psychological needs (e.g., for reassurance).  If the element of surprise and perpexity is absent, these kind of experiences might be better termed "anomalous familiarity" (like when you find someone's face familiar but cannot quite place where you know her or him from).
2. Paranormal
   These exhibit precognitive knowledge ("I knew what he was going to say or do before he did it!"), ("I remember that she was going to do that!"), ("I knew what was inside the house or around the corner before I went there!") or telepathic knowledge ("I suddenly knew what she or he was thinking!"). These are not usually associated with a pathological condition.   Those wishing to know more about precognition might be interested in learning about the experimental work that Prof. Daryl Bem has done (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4706048/) and also the research that has been published by Dr. Dean Radin (http://deanradin.com/evidence/Radin2011AAAS.pdf) at the Institute for Noetic Sciences.
3. Pathological
   A condition is said to be pathological when it causes suffering.  One pathological condition in which déjà experiences sometimes occur is epilepsy of the temporal lobe. In many neurological and psychiatric textbooks it is often the only pathological condition mentioned in connection with déjà vu. With temporal lobe epilepsy, in addition to the déjà experience, there are usually other symptoms such as nausea, headache, smelling bad smells, and even fainting. As Dr. Chari pointed out, there are a number of other ailments that can also produce déjà experiences. His list (given in Neppe's book on page 25) also included "alcoholic psychosis, migraine, schizophrenia and paranoia, general paresis, and psychoneurosis. It would seem that emotional stress can also precipitate déja experiences. Recent work by Dr. Chris Moulin, Leeds University, has shown that demented patients sometimes complain about a persistent sense of familiarity which he has called "chronic déjà vu".  If the frequency, intensity and/or length of the déjà experience is such that it is distressing for the individual having it, one could say that this is pathological and some form of treatment should be considered.
4. Evoked
   Down through the years there have been attempts at reproducing déjà feelings in the laboratory.  The earliest work (Banister & Zangwill, 1941) used hypnosis and this approach is being explored again in the work at Leeds University (O'Connor,Barnier & Cox, 2008).  Stimulation with electrodes to evoke déjà-vu-like experiences during open-brain surgery has also been tried with modest success (Penfield, 1958, Bartolomei, 2004).  Recently, there have also been reports of déjà experience being triggered by certain drugs, recreational and otherwise (Taiminen & Jaaskelainen, 2001).

Types of Déjà Experience

On page 10 of his book, Dr. Neppe lists 20 different types of déjà experience. He writes:

"There are many ways in which déjà experience may manifest. Some of these have specific names:

"At times the demarcation is artificial, as the déjà experience can coexist in more than one of the above [types]. Moreover, the literature and my experience indicate that there are several other common kinds of déjà experience that have not yet been categorized. New terms are suggested:

And for completeness, one should be sure and include déjà vu (already seen).

Those with a good knowledge of French may quibble with these definitions and we'll be happy to modify them accordingly. Other forms of déjà experience may come to mind; they will be welcome as well.

As to which are met with most often, no one can say at this point in time. In my paper, Three Types of Déjà Vu(Funkhouser, 1995), I tried to delineate the differences between déjà vécu, déjà visité and déjà senti because I thought these forms of déjà experience were the ones encountered most often. It is not really known, however, if that is true. One of the purposes of this website is to collect data so that this question can be answered (at least for those who find their way to this website).

Among those terms used to designate déjà experience have been: fausse reconaissance or memoire (false recognition or memory), paramnesie (paramnesia), reminiscence or pseudo-reminiscence, Bekanntheitsgefühl(familiarity), Erinnerungs- fälschung or täuschung (memory falsification or illusion), memory hallucinations, or Doppelwahrnehmung or -vorstellung (double perception or imagination) ~ depending on the investigator's language and area of interest. There even exist negative or reversed forms in which the person denies recognizing what must be familiar or claims not to remember having said something which others are sure that he did. These phenomena are designated jamais vu and jamais raconté (never seen or told) (see following section).

Related Phenomena

• Jamais vu (never seen): the sudden feeling that what should be familiar isn't. 
• Presque vu (almost seen): The feeling that you can almost remember something but it just won't come to mind. It is related to the so-called “tip of the tongue” phenomena.
• Capgras Syndrome: the afflicted person is convinced that those he or she is familiar with have been replaced by impostors.
• Fregoli delusion: a rare disorder in which the afflicted person is convinced that many or all of the people he or she meets are really one person in many disguises.
• Paramnesia: a disorder of memory in which dreams or fantasies are confused with reality
• Reduplicative paramnesia: The person is convinced that everything is being repeated; everything is familiar.
• Restricted paramnesia: A feeling of familiarity in which one is unable to come up with the source. One has the feeling that one should recognize or know the place, object or person but is unable to tie him, her or it to a specific incident or location from the past. (Bannister & Zangwell, 1941). The feeling can extend beyond the person, object or place to take in the whole situation (cf. http://www.thelastreflexdejavu.blogspot.com/2008/08/memory-explanations-part-2.html )
• Redintegration: Seeing (hearing, tasting, touching, smelling) a person, object or place can evoke an entire memory sequence. For more information, see http://en.wikipedia.org/wiki/Redintegration.
• Precognitive dreams: Dreams that in some way (in detail or symbolically) foretell what is going to happen in the future. These are remembered (and possibly even written down) before the pre-dreamt events occur.
• Premonition: According to Webster, a forewarning, a foreboding, a presentiment.
• Intuitive hunches: According to Webster, a feeling about something not based on facts; premonition or suspicion. 
• Mistaken identity: A conviction that you know or recognize someone and it turns out that this is wrong.
• Reincarnation: The impression or conviction that one has lived in a place before.
• Out-of-the-body experiences: The experience of leaving and moving outside the body.
• Telepathy: Having the impression that the thoughts one is thinking have been sent by someone else.
• Clairvoyance: A mental impression of seeing a place or event that is far away.
• Synchronicity: A term coined by C. G. Jung that refers to meaningful coincidences that seem to have no apparent cause (i.e., said to be "acausal").  More information about sychronicities is available in a Wikipedia article about them.

At the moment this is very sketchy and will hopefully be filled in with more material and examples later. 

Much more information is available in the déjà vu experience by Alan S. Brown. There is also more information at the Top 10 Strange Phenomena website.