The science blog Cosmic Variance has a great rundown of what the LHC could find. At the top of this list is the Higgs boson, which is the only particle in the Standard Model (the theory that describes the fundamental interactions between the particles that make up all matter), that hasn't yet been detected. The site thinks there is a 95 percent chance the LHC finds this particle, and that could lead to a much better understanding of how our universe works. Other notable possibilities on Cosmic Variance's list include finding extra dimensions (these could be so-called "warped" hidden dimensions...