I am not an expert on the following aspect of LHC, so I'll bring it up but hope others will elaborate (feel free to use the community wiki features!):
One of the major contributions of LHC has been to develop better data-management technology. LHC generates way too much data to store, let alone to transmit, and so quite a lot of statistics, mathematics, and computer research went into designing hardware that makes instantaneous decisions about what data to save. Once the robot has culled the data, transmitting it to humans for further processing is quite a task, and it's reasonable to think that the hardware developed to do so will provide one of the models for a next-generation internet.