No.
The Higgs boson is not dangerous and will not destroy the universe.
The Higgs boson is a type of particle, a little ripple in the Higgs field. [See here for the Higgs FAQ.] This lowly particle, if you’re lucky enough to make one (and at the world’s largest particle accelerator, the Large Hadron Collider, only one in a trillion proton-proton collisions actually does so) has a brief life, disintegrating to other particles in less than the time that it takes light to cross from one side of an atom to another. (Recall that light can travel from the Earth to the Moon in under two seconds.) Such a fragile creature is hardly more dangerous than a mayfly.
Anyone who says otherwise probably read Hawking’s book (or read about it in the press) but didn’t understand what he or she was reading, perhaps because he or she had not read the Higgs FAQ.
If you want to worry about something Higgs-related, you can try to worry about the Higgs field, which is “ON” in our universe, though not nearly as “on” as it could be. If someone were to turn the Higgs field OFF, let’s say as a practical joke, that would be a disaster: all ordinary matter across the universe would explode, because the electrons on the outskirts of atoms would lose their mass and fly off into space. This is not something to worry about, however. We know it would require an input of energy and can’t happen spontaneously. Moreover, the amount of energy required to artificially turn the Higgs field off is immense; to do so even in a small room would require energy comparable to that of a typical supernova, an explosion of a star that can outshine an entire galaxy and releases the vast majority of its energy in unseen neutrinos. No one, fortunately, has a supernova in his or her back pocket. And if someone did, we’d have more immediate problems than worrying about someone wasting a supernova trying to turn off the Higgs field in a basement somewhere.
Now it would also be a disaster if someone could turn the Higgs field WAY UP… more than when your older brother turned up the volume on your stereo or MP3 player and blew out your speakers. In this case atoms would violently collapse, or worse, and things would be just as nasty as if the Higgs field were turned OFF. Should you worry about this? Well, it’s possible this could happen spontaneously, so it’s slightly more plausible. But I do mean slightly. Very slightly.