I don't buy those theories. They go against common sense.

Sorry, but that's just... oh, wow.
First of all, common sense is highly overrated in physics, particularly particle physics and quantum phenomena (and, to lesser extent in relativity theory). That's because common sense applies to macroscopic world which our brains have adapted to work in, which means pretty much just electromagnetic interaction and gravity. The common sense applies to quantum scale pretty much as much as Kant's categoric imperative applies to a bunch of plankton. Things don't work along common sense just because we'd like that, welcome to the universe.

Secondly, how much energy do you need to explode a bunch of trinitrotoluene, or hexotol?
The question of energy required for "destruction" depends of the definition of destruction. I'd say causing a fundamental matter phase/consistency change and causing things to fall apart to form a lump of particles classifies as destruction, but more of that further on the Strangelet section... it's not the absolute amount of energy that troubles some people, but the "uncertainty" about how that condenced energy will act and react with it's surroundings. "Uncertainty" in quote marks because it's rather certain that the energies produced in LHC won't cause things to fall apart - but aside from that the knowledge is hazy.
So, like said, it's not the question of energy required for complete obliteration that worries some people - all the possible apocalypse hypotheses in this case don't require much energy per ce - except for the black hole argument, in which case it's proposed (AFAIK) that the generated black hole could by chance hit a suitable mass concentration, eat it up, strengthen, eat more and end up groving faster than evaporating as Hawking radiation. But, as pointed out, this chance is unlikely because the LHC pretty much just mimics the already existing high energy particles in controlled environment. It doesn't do anything that the universe isn't doing to us all the time.
Hell, there have been observations about protons that have had kinetic energy equivalence of a
brick falling to your feet from about one metre height. LHC can't go
anywhere near that kind of energy yield, and there are that kind of particles coming down on us all the time... well, energies that high are rare, but the point is that high energy particles hit each other all the time with higher energies than will happen in LHC experiments, so it's very likely we don't end up destroying the universe.
The other hypothesis of generating strangelet particles doesn't rely on energy either, but rather a transmutative hypothesized nature of these particles. The idea is that these strangelet particles could perhaps be able to change normal matter to strangelet matter, changing the way it behaves, which would pretty much stop or at least change all the chemical reactions and probably cause life as we know it to end. However, there's really no experimental or much of a theoretical basis for this hypothesis - and, again, there's the fact that we're under constant cosmic ray bombardment similar by particles of similar or higher energies that will occur in LHC, and we haven't changed into strangelet particles so far.
I kinda agree on the part that people who don't know how stuff works in particle physics have all right to be a bit worried when some guys flail their hands around with a death note on other and a PhD on other, spouting apocalypse predictions from their mouths (exaggerated for the lulz but you get the picture). It's okay to worry about safety, but on the other hand there's the consensus of the scientific world that
"All that will happen in LHC has happened before, and will happen again", and thus far it hasn't caused the destruction of the world.
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Perhaps it would be good to explain a bit on how LHC works and what it will be doing. Basically it's a circle shaped tunnel with magnets around and vacuum inside. The magnetic and electric field(s) can be used to accelerate and direct charged particles (usually large hadrons like protons) and then they are directed into a bubble chamber* - or other experimental devices such as wire chamber, spark chamber or silicon detectors, depending on the experiment at hand, doesn't really matter in this context though - where they hit other particles, and the actual research will look at what happens when the particles break into other particles, and how they interact with each other.
Now consider that this is, in basics, normal occurrence in universe. The only difference is the scientific equipment around the collision area set up to record events. There is
very little probability that the scientists could trigger something that hasn't happened in about 4+ billion years of Earth's existence and cause a fundamental change in matter consistence. Exotic particles are formed and colliding with each other all the time somewhere, the only difference LHC makes is that it can repeat the experiments with constant energy particles and thus the analysis gets more accurate.
It would be possible to just build bubble chambers all over the place and wait for cosmic rays to hit them, but it would be difficult to repeat the experiments to calibrate results because the cosmic ray particles tend to have a lot of variation in energies. Fundamentally there would be nothing different in it, though, and LHC offers the benefit of controlled circumstances and thus a lot more accurate research results.
Cosmic rays will still be researched as well, precisely because even LHC can't build up energies that high.
*Bubble chamber is basically a chamber filled with superheated, transparent liquid - usually hydrogen. When a charged particle traverses through this matter, it creates an ionized path in it's track. This can be photographed by high speed cameras and/or the light flashes registered with other type of sensors with less resolution but more sensitivity. The tracks of particles form pretty lines, curves, spirals and flashes. From the projection of trajectories, it's possible to analyze a lot of properties of the particles - such as mass, spin, electric charge and other stuff.
Wire chamber (or drift chamber) is basically a three-dimensional geiger counter on steroids - it can track higher energy particles better than a bubble chamber, and no photographs are made like in bubble chamber. The research data is pretty much digital.
Spark chamber is a detector based on observing flashes caused by particle interactions.
Silicon detectors are basically diodes or arrays of diodes set to detect varieties of radiation, either particle or electromagnetic.