No, NLP is not a cult.  Indeed, it isn't clear where this claim originated.  The following explanation could be true, but don'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 are a mixture of information from a single NLP training company, and his own assumption that if two things look alike, no matter how superficially, 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)
    
   This line of reasoning makes as much sense as saying "Quite a few postmen are Roman Catholics therefore being a postman must be part of the Roman Catholic religion."  It is the postmen who follow the religion, not the religion that follows the postmen.
   In practice, working details of many (or most?) of the basic NLP techniques can be found in literally dozens of books available in bookstores.  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', and no such organizations, other than Insight, are named in support of the claim.
    

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, 'similar sentiments' - a claim for which he offers 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 perople 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 their educational antecedents, 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 "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 (when one of the co-creators was still a school boy)!

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?

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.

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.