I'm more involved in the analysis / software side of research, and somebody who is working on hardware can probably tell you more about technology spin-offs. In fact, I'd like to hear about them, too.
One thing that has been pioneered at the LHC is grid computing. Basically we were doing cloud computing before it was cool. Of course, the requirements of science and industry are different, and we were quickly overtaken in scale by Amazon, Google, etc.. But still, particle physicists were among the first to connect different data centers across the world to a unified resource. You just say "do this computation on this dataset" and the system finds the optimal place to perform the calculation without copying too much data around, and delivers the packaged up datasets back when it's done.
Many spin-offs are small improvements of existing technology, giant leaps are rare. An example of an incremental step are improved solar panels [1] using LHC vacuum technology. There is also a lot of work done on superconductors and magnets that is cutting-edge, but I don't know if it has found application yet.
We have a lot of hardware development that is really interesting, but too far away from consumer electronics to be used as a spin-off, like radiation hard electronics, or high precision particle detectors. Maybe some of this will go into medical devices.
We used to be early adopters of machine learning (e.g. neural networks) and pattern recognition techniques, but have been utterly surpassed in these fields by industry recently, and are only starting to import modern techniques, like deep neural networks.
[1]: http://www.symmetrymagazine.org/breaking/2012/03/16/cern-spi...