No, NLP is not a cult.  Indeed, it isn't clear where this claim originated.  The following explanation could be true, but I wouldn't 'bet the farm on it'.

Who says NLP is a Cult?

In 1996, a book entitled Sects, 'Cults' & Alternative Religions, written by a David V. Barrett, was published, which included a section on what Barrett thought NLP was about.

In fact Barrett seems to be the kind of person who can't tell the difference between a menu and real food, so to speak, and his views on NLP appear to be based entirely on a mixture of (a) information from a single NLP training company, and (b) his own assumption that if two things look alike, no matter how superficial the similarity may be, they are alike.  In fact Barrett makes three rather irrational allegations about "NLP":

1. "... several movements which do have a spiritual element, such as Insight (see p. 239) openly use NLP techniques and have NLP Masters [sic] among their leaders."
   (page 237)

But what valid point is Barrett making here?

Firstly, we should note that Barrett only supplies the name of one "movement" which allegedly fits his description.  At this stage of his argument, then, the existence of any other such groups is therefore entirely hypothetical.

But let's suppose, just for the sake of the argument, that there really are other groups and other people who fit the description.  Barrett hasn't actually presented us with evidence of anything at all which would support his overall argument.  To make the point, let's make a small change in Barrett's wording and see what effect it has:

"... a substantial number of coaches openly use NLP-related techniques in their work, and some are NLP Master Practitioners."

Since this is undoubtedly true - the University of Derby runs an accredited MA course in Applied Coaching - can we take it that "NLP" is actually a form of coaching?
Surely not.

In practice, the FoNLP (field of NLP) is first and foremost about communication skills.  The kind of skills which can be usefully applied in a wide range of contexts.

Moreover, working details of many (or most?) of the basic NLP-related techniques can be found in literally dozens of books available in run-of-the-mill High Street bookstores.  And no one is required to describe their personal beliefs before they are allowed to buy a book on the subject.

Likewise companies offering training in NLP and NLP-related techniques do not 'vet' potential trainees to weed out people because of their special interests or affiliations.  Thus the use of NLP-related techniques is in no way restricted to any specific group of people.
Nor does Barrett provide any evidence that the use of NLP techniques has anything to do with the 'spiritual element' of any such 'movements' or organizations.
For evidence which rebuts Barrett's claim see the comments by co-creator of the FoNLP, John Grinder. later on in this FAQ.
Just before that, let's watch as Mr Barrett digs himself in a little deeper:

2. "... although it should be stressed once again that NLP itself is a process, a set of techniques, a methodology, and not a religious movement, or even a religious belief system, its function is similar to that of a religion ... NLP offers specific and practical ways of making desired changes in our own and others' behaviour.  It is about what works.  Similar sentiments can be found in many Esoteric religious movements ..."
   (page 237).

If we believe this claim then any training course is an inherently "religious" activity!
 
It would be interesting to know at what point, in Barrett's imagination, an alleged, and marvellously vague 'similar[ity of] sentiments' - a claim for which he offers no description and no coherent evidence - become a reason to assume that two very different fields are in any sense identical?  This isn't even 'guilt by association', it is 'guilt by imaginary association'.

3. "Interestingly, the brief biographies of NLP Trainers always [sic] give the names of the people they themselves trained under.  This could be seen as similar to new Eastern-origin religions tracing themselves back through a progression of gurus, and Esoteric movements claiming the authority of authenticity through their descent from previous movements"
   (page 238).

This, I'm afraid, is sheer nonsense.

• In the first place Barrett states, in the first paragraph of this section, that "The information here was provided by John Seymour Associates ..." (page 237).  So is it Barrett who allegedly knows what ALL NLP trainers do, or someone at JSA?  For what it's worth, when I did a straw poll via Google only about two-thirds of the trainers included the name of even one person or company with whom they trained;
   
• What sensible comparison is there between citing one or two people whom you have trained with, and Barrett's "progression of gurus"?
   
• It appears to have escaped Barrett's notice that academics routinely list brief details of their educational qualifications, at least from their first degree onwards.  If his allegation is true then we should presumably hold that all university faculty members are following the path created by these unidentified "new Eastern-origin religions ... and Esoteric movements."
  Somewhat ironically, one academic has actually included a very lightly edited version of Barrett's article in his own book on the subject of alternative religions - even down to the claim that if you mentioned who you trained with that's like being part of a new Eastern-origin religion, etc. (see The Mystic Sociologist).

Back to front down under

A second possible candidate as the origin of this myth may be an article in an Australian newspaper.
Although this article purported to be a serious discussion of cults in Australia, it turned out to be not much more than hype for a rather hysterical-sounding, soon-to-be-published book by a local psychotherapist.  Its accuracy can be judged by the fact that it described NLP as originating in America in the mid-1970s (correct) but only after claiming that NLP had been around since the 1960s (at which time one of the co-creators would still have been in school)!

The article was cited on the Wikipedia NLP page and in the list of references for a Knol article on NLP that basically consists of cut and pasted elements from the Wikipedia page.  However the reference has now been dropped in both cases and so far I have not been able to find it again through Google.

Why NLP is NOT a cult

According to one web site that carries accurate and useful information about cults (see the Cult Information Centre):

"Every cult can be defined as a group having all of the following five characteristics:

1. It uses psychological coercion to recruit, indoctrinate and retain its members;
    
2. It forms an elitist totalitarian society;
    
3. Its founder leader is self-appointed, dogmatic, messianic, not accountable and has charisma;
    
4. It believes 'the end justifies the means' in order to solicit funds and recruit people;
    
5. Its wealth does not benefit its members or society.

Having investigated a number of cults myself, over a period of more than 10 years, in my opinion this is as good a basic definition of a cult as we are likely to find, though I would like to add one further characteristic:

6. It has a policy of isolating its members, both mentally and in many cases physically, from anyone outside of the cult, including (especially?) close friends and family members."

And that being the case, how does NLP measure up as a cult?  Whereas cults invariably create a number of physical "centres" (cult-owned buildings) in the areas where they operate, the various elements within the NLP-related community are very loosely organised and - so far as I know - have no means of isolating people, either physically or mentally.

1. Does it use psychological coercion to recruit, indoctrinate and retain its members?
    
   Since there is no central organisation to join, clearly people cannot be "recruited" to NLP in the sense that a genuine cult recruits members.  By the same token, since there are no "members" they cannot be "indoctrinated" in order to "retain" them.
    
2. Does it form "an elitist totalitarian society"?
    
   Whilst it is true that some people may imagine that being trained in NLP-associated techniques makes them superior in some way, this is a misconception and there is nothing vaguely resembling "an elitist totalitarian society" within the field of NLP.
    
3. Does it have a self-appointed founder leader who is dogmatic, messianic, not accountable and has charisma?
    
   Whilst a certain amount of hero worship goes on amongst some sections of the NLP community, since there is/are no overarching organization(s) controlling NLP-related activities, to be strictly accurate, NLP has no "founder", let alone "founder leader," in the sense that it is used in this definition.
   Richard Bandler originated what is now known as NLP, and Bandler together with John Grinder were the original co-creators.  Neither of these people, so far as I know, has ever claimed to be a re-incarnation of Jesus or any other "messianic" figure, though some NLP seminar ads have implied that Bandler is to NLP what Mozart was to piano playing - in a teaching capacity, that is.
    
4. Does it believe that 'the end justifies the means' in order to solicit funds and/or recruit people?
    
   Again, there is no central body so there is no one to "solicit funds" - though naturally companies offering NLP-related training usually charge for their courses, and NLP-related "professional bodies" such as the Professional Guild of NLP charge subscription fees in the same way as professional organisations in any other activity.  Still, there are no "solicited funds" (donations) involved.
    
5. Does it accumulate wealth that does not benefit its members or society?
    
   No central organization, no "solicit[ed] funds", so no "wealth" which could be accumulated.
    
6. Does it isolate 'NLPers' mentally, physically or both from anyone who is not an 'NLPer'?
    
   Even NLP training seminars are usually held in public locations - hotels, hired university facilities, etc. - as few training companies have room for groups of more than a dozen or so people, if any.  Moreover, whilst some people go on numerous NLP-related training courses (one or two every year), it is likely that the majority of NLPers have only been on one or two courses (an 'introductory' or 'taster' and a 'practitioner' course, or a 'practitioner' and a 'master practioner' course) in all their time as members of the NLP community.  In addition to the courses or seminars there are NLP 'practice groups' in some towns and cities which meet regularly - usually for just one evening per month.  And finally, there are a number of online 'chat groups', though even the largest such groups are unlikely to number more than a few thousand members, the vast majority of whom tend to be 'lurkers' - people who may read posts that seem interesting to them, but who otherwise take little or no active part in the group.
   But perhaps the crucial influence is the fact that NLP and the NLP-related techniques are primarily concerned developing an individual's communication and social skills.  For NLPers to be isolated from the wider community would therefore be illogical and totally self-defeating.

NLP and "Spirituality"

Let me start by saying that I personally know of at least half-a-dozen people, quite well-known within some parts of the NLP community, who have tried to invest "NLP" with a layer of spirituality.  None of them, however, has been successful in establishing their ideas as part of the catalogue of authentic NLP-related concepts.
The most widely-known member of this rather exclusive, and misguided fraternity is Robert Dilts, and it is a response by John Grinder, a co-creator of NLP and the FoNLP (field of NLP) to Dilts' claim that he had, "helped connect NLP to deeper aspects of life such as spiritual aspects" (Dilts, PNNL Repere Interview, 2004).  Grinders comments establish beyond any reasonable doubt the NON-involvement of authentic NLP in any form of religion or spirituality:

Mr, Dilts, in spite of the direct tutelage offered by each of the co-creators of NLP has managed to miss the point with astonishing consistency.  It is precisely because there is no requirement to subscribe to particular beliefs and values that NLP moves so easily across cultural and linguistic barriers and is easily and respectfully incorporated into these distinct systems.  What he is taking credit for is a degradation of the very technology in which he makes his living. ... A modeling, for example, of the processes by which our species in its apparently compulsive search for the illusion of stability and security generates and then embraces its own creations - the beliefs, values and "deeper aspects of life" … - would be a brilliant and useful piece of modeling work - but to arbitrarily present a PARTICULAR SET - any specific set of values, beliefs and even hierarchies of these amazing creatures - as if they had some validity and/or stability across individuals let alone distinct cultures is a travesty and an imposition of content.  The mentioned characteristics leave such work far, far below the minimum ethical and precision standards that have allowed NLP to flourish.  Yes, a modeling of the PROCESSES by which we as humans create such constructions would be a legitimate and likely useful task but to fall to the level of imposing one's own beliefs, values ... is quite astonishing.
(John Grinder (2005).  Review of an Interview with Robert Dilts, in the French NLP magazine PNL Repere, January 2006)

Conclusions

In short, no, the NLP community doesn't constitute any kind of 'cult' in the normal meaning of the word.  Though it is also fair to say that there are certainly people involved with FoNLP (field of NLP) who, as in almost any field of human activity, tend to exaggerate the importance and efficacy of the techniques they have learnt about, and the brilliance of certain NLP trainers.  This behaviour is, however, under the control of the individual and is certainly not inherent within NLP and the NLP-related techniques.

Just as it would be wise to treat exaggerated claims about the benefits of NLP with a hefty dose of scepticism, it would be equally advisable to disregard the claims of the self-styled experts who, in describing the FoNLP as a cult, only demonstrate that they are misinformed about cults, or the FoNLP, or both.

CAVEAT
Whilst the FoNLP is not itself a cult, it is true that some cults have used and/or are using techniques similar to those used in the FoNLP.  Given that the techniques in question are all in the public domain, and most have been described in numerous books, magazines, etc., it should not supposed that this "sharing" of ideas means that the originators, developers or NLPers in general, encourage or sanction the misuse of any NLP-associated techniques on any person or group for any reason.
The concept of using NLP-associated techniques to produce beneficial, win/win results, has been a generally accepted standard from the earliest days of NLP's development.  Anything else is a violation of the voluntary but widely agreed standards prevalent within the NLP community.