The short answer to the posed question is: "No, the LHC will not destroy the Earth"
The Large Hadron Collider is being used to collide protons together in an effort to open up new doors to the particle physics world. On September 10th, 2008, scientists at CERN "turned on" the LHC, and the first complete circuit of protons was a huge success. In October, they will begin actually colliding the particles. Here is where there seems to be a serious concern over the potential destruction of the planet.
The cries reaching various points of the internet warn of a supposed black hole that will break free of its constraints and suck up the earth, along with all of us. Just typing that makes me chuckle slightly. I am no particle physicist, but that didn't stop me from doing my own small research on the subject.
Micro black holes DO have the potential to form - in fact, CERN scientists admit that not only is it likely, but micro black holes will probably form around one per second. That seems like a lot, but never fear, the Earth is not about to be engulfed by a runaway LHC.
Steven Hawkings, arguably the most famous scientists of our times, proposed his theory on black holes a few years back. He proposed that the inside black holes are not simply "empty space" controlled by gravity, and that over time, black holes bleed themselves out. Depending on the size of the black hole depends on the time it takes for the black hole to die. This accepted theory is known as "Hawkings Radiation".
Micro black holes are subject to Hawkings Radiation just as much as "normal" black holes. Considering CERN scientists interviewed for the History Channel stated that if a black hole forms it will be "the size of, oh, a proton", one can imagine it will take but microseconds for said black holes to disappear. At most, a slight flash of light may occur during the process as the black hole dies. It is physically impossible for any micro black hole formed by the LHC to pose a threat to humanity.
CERN also went so far as to call the original scientist who proposed this idea of the LHC destroying the human race a "moron", and I for one would like to think that the people dedicated to this machine for decades now would have thought about this idea before and dismissed it - they would never agree to propose such a test if there was any chance the Earth would be destroyed in the process. Where is the value in that?