Will negatively charged strangelets be produced by the LHC? Witten (and earlier, Bodner) hypothesized that strange matter (up, down, strange quarks) should be more stable than "regular" nuclear matter(The strange matter hypothesis). That is that the typical hadrons in matter are metastable, and will eventually decay into strange matter because it can exist at lower energy configuations.
There was some publicity about strangelets as a disaster scenario for the RHIC and the LHC, and a very interesting paper was commissioned by the Brookhaven National Laboratory to evaluate risks of various disasters possible in the RHIC: The authors are Busza, Jaffe, Sandweiss, and Wilczek. A conclusion is that positively charged and neutral strangelets would be no problem, and that negatively charged ones, which would be a huge problem because they would convert all the nuclear matter to strange matter, would be very unlikely based on cosmic ray evidence (ie lack of them) and other considerations. There are theories that strange matter occurs in the cores of neutron stars and may convert them completely resulting in denser, smaller stars than predicted for nuclear matter, but I am not sure.
Do we expect the LHC to produce negatively charged strangelets? I think the answer to the question is NO, none will be found or produced, but the reasoning from cosmic rays is not definitive imo( I guess I should have said, "but asymptotically close to it"--G). The Jaffe paper above has merit I believe not just as a physics document, but also as public relations, and has historical value, so I wanted to draw attention to it.
 A: Dear Gordon, apologies but I think that the paper by Busza, Jaffe, Sandweiss, and Wilczek is very robust. In particular, it is a physics paper, not a public relations paper, and one could argue that your comment claiming otherwise may be offending to the authors. It is a physics paper about a question that physicists usually consider funny so most physicists don't really study this topic seriously but these four authors did study it seriously. The paper is "less technical" and looks "softer" than many other papers by these and similar authors but that's not because they did a bad job; it's because the very topic of the paper is an amusing schoolkid's conspiracy theory, not a cutting-edge question about state-of-the-art physics. So the relevant arguments may be accessible to the schoolkids, too. But that doesn't mean that they're wrong.
The answer to your question whether the LHC will produce negatively charged strangelets is obviously No, at a 99.9999999999+ percent level.
I don't know what exactly you find unsatisfactory about the paper - and, sorry to say, I agree with David that it is not a good approach to pose a "question" in which you just declare that you don't trust a paper, without offering a glimpse of a rational reason - but the paper actually mentions many other reasons why the answer is No - not just the cosmic rays argument.
The cosmic rays are arguably the most waterproof reason why this hypothetical catastrophe - and pretty much any catastrophe of this type - has to be wrong. It is waterproof exactly because it is phenomenological in character and only depends on the observation of a long-lived Universe with long-lived stars etc. It doesn't strongly depend on our theoretical assumptions. So even if we're making some incorrect assumptions, it's still true that planets can't be destroyed in this way because this would have happened many times.
However, if you allow theorists to actually trust their theories, which is what they're allowed to do in all other papers (papers in scientific disciplines that have found something can't start and don't start from scratch), there are multiple other reasons why it can't happen (and they're described in the paper), namely


*

*QCD overwhelmingly indicates that the metastable stranglet matter of the relevant size would be positively charged; see e.g. http://arxiv.org/abs/hep-ph/0008217

*The matter would be unstable for small sizes - because of destabilizing surface effects

*Strangelets are not easily produced by hadron-hadron collisions

*Strangelets have never been seen in the outer space at all; the neutron stars collapsed into the stable strangelet matter (as you mentioned) would be called "quark stars" but they haven't been seen yet


Some research also indicates that strangelets can only be locally stable but they're not ground states similar to the nuclei, see e.g. http://arxiv.org/abs/hep-ph/0604093 ... Another paper leads to mixed results about this question: http://arxiv.org/abs/hep-ph/0209184 ... Also, strangelets failed to appear in various collision experiments, see e.g. STAR Collaboration 2005 (gold-gold) http://arxiv.org/abs/nucl-ex/0511047 ... Quark-gluon plasma was hypothesized to be linked to the Centauro events, see e.g. http://arxiv.org/abs/hep-ex/0209008
Pretty much every point above would be enough to conclude that those stable strangelets can't be produced, and if you really believe that they will be produced, I can offer you 1,000:1 odds to get "insured". In recent years, it has become popular to indefinitely spread myths about various hypothetical catastrophes caused by "small events", regardless of the actual physics evidence that such catastrophes can't occur, but I don't think this server should adopt this approach.
Concerning your question whether the "Bodner-Witten" (I would also add Farhi and Jaffe) strange quark matter (SQM) hypothesis is correct, it depends what you exactly mean by this hypothesis. If you just mean that SQM as a form of quark-gluon plasma (QGP) has a lower energy density than the nuclear matter, then it looks relatively likely (but surely not guaranteed), and supported by lattice QCD etc. If you mean that it can be found somewhere in the Universe, the answer is we don't know, but if it's somewhere, it's in artifacts of supernova explosions and gamma-ray bursts (which provide the particles with a sufficiently extreme environment). If you mean the hypothesis that SQM is negatively charged and a part of ordinary stars and solar systems such as ours, the answer as seen by the contemporary science is almost certainly No. It's very important to distinguish those different propositions and questions, exactly because their conflation leads to irrational fears etc. (The same disclaimer holds for the the global warming threats or any other catastrophe scenario. One must be very clear about what he means that e.g. "global warming is real" because different questions have different answers.)
The paper by Busza et al. offers 20+ pages of evidence that such things can't happen, and the cosmic-rays argument is just the most waterproof one among them. And of course, it's a whole paper because it's meant to be much more detailed and careful an analysis of the question than one answer or several answers on a Physics Stack Exchange. It's just not quite kosher to de facto deny that those 20+ pages exist and to offer one paragraph without any technical content that tries to suggest that the paper is not robust.
A: What Lubos said. 
There was also a big brouhaha about black holes produced by the LHC a while ago in the news. I read the report, and it was written before the large string dimension black holes that people hope to see at the LHC. The cosmic rays summary in the paper would cover this disaster also.
Of course it is a type of anthropic principle: since the universe has reached 14+billion years and we exist then such catastrophes are very very rare.
I remember back in the beginning 1980's when proton decay was the fashion. At the same time lasers and induced de excitations of pumped crystals were still new. I remember some  worry, after realizing that we are sitting on a pumped up ball of putative decay products of proton decay; until putting down the numbers and seeing that we are saved by the very small value of hbar.( another anthropic input).
We already have a quark gluon plasma at the LHC :). I do not think that strangelets are in the program. There is a report on this.
My answer is no, there is no danger . 
